Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

The effects of the generalized use of iodized salt on occupational patterns in Switzerland.

This paper examines the impact of salt iodization in Switzerland in the 1920s and 1930s on occupational patterns of cohorts born after the intervention. The generalized use of iodized salt successfully combatted iodine deficiency disorders, which were previously endemic in some areas of Switzerland. The most important effect of universal prophylaxis by means of iodized salt was the eradication of mental retardation inflicted in utero by lack of iodine. This paper looks for evidence of increased cognitive ability of those treated with iodine in utero by examining the occupational choice and characteristics of occupations chosen by cohorts born after the intervention. By exploiting variation in pre-existing conditions and in the timing of the intervention, I find that cohorts born in previously highly-deficient areas after the introduction of iodized salt self-selected into higher-paying occupations. I also find that the characteristics of occupations in those areas changed, and that cohorts born after the intervention engaged to a higher degree in occupations with higher cognitive demands, whereas they opted out of physical-labor-intensive occupations.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

Generalized inductive limits of quasidiagonal C*-algebras

If A is a unital quasidiagonal C*-algebra, we construct a generalized inductive limit BA which is simple, unital and inherits many structural properties from A. If A is the unitization of a non-simple purely infinite algebra (e.g., the cone over a Cuntz algebra), then BA is tracially AF which, among other things, lends support to a conjecture of Toms.

Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

On Borel equivalence relations in generalized Baire space

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On a supremum operator

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Local Distance-Based Generalized Linear Models using the dbstats package for R

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models firstly with the generalized linear model concept, then by localizing. Distances between individuals are the only predictor information needed to fit these models. Therefore they are applicable to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. Models can be fitted and analysed with the R package dbstats, which implements several distancebased prediction methods.

On spectral properties of the modified convolution operator

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On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.