The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

On absoluteness of categoricity in abstract elementary classes

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Hankel operators on holomorphic Hardy-Orlicz spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Potential isomorphism of elementary substructures of a strictly stable homogeneous model

"Vegeu el resum a l'inici del document del fitxer adjunt."

Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Intergovernmental Transfers and Elementary Education: Quasi-Experimental Evidence from Brazil

Whether providing additional resources to local communities leads to improved public services and better outcomes more generally, given existing management capacity and incentive and accountability structures, is an unresolved yet important question for public policy. This paper uses a regression-discontinuity design to evaluate the effect of unrestricted fiscal transfers on local spending (including on education), schooling and learning in Brazil. Results show that transfers increase local public spending almost one for one with no evidence of crowding out own revenue or other revenue sources. Extra per capita transfers of 1000 Reais lead to about 0.42 additional years of elementary schooling and student literacy rates increase by about 5.6 percentage points on average. Part of this effect arises through higher teacher-student ratios in municipal elementary school systems. Results also suggest that additional resources have stronger effects in more rural and less developed parts of Brazil.

Toolbox to Address Safety and Operations on School Grounds and Public Streets Adjacent to Elementary and Middle Schools in Iowa, August 2006

This study identified transportation safety issues at existing Iowa school sites through on-site observations, traffic data collection, and through interviews with schools, law enforcement, and traffic engineers. Frequently observed problems, such as crossing at unmarked crosswalks, unloading and loading students on the street side, inattentive student safety patrols, and illegal parking, were documented and solutions were recommended for implementation. The results of the study also conclude that regular communications between school officials, traffic engineers, law enforcement, parents, and school transportation personnel are all critical to promoting safe operations within school zones.

Addressing elementary school teachers' professional stressors: Practical suggestions for schools and adminstrators

Purpose: Given the preponderance of education reform since the No Child Left Behind Act (U.S. Department of Education, 2001), reform efforts have shaped the nature of the work and culture in schools. The emphasis on standardized testing to determine schools' status and student performance, among other factors, has generated stress, particularly for teachers. Therefore, district and school administrators are encouraged to consider the contextual factors that contribute to teacher stress to address them and to retain high-performing teachers. Research Methods/Approach: Participants were recruited from two types of schools in order to test hypotheses related to directional responding as a function of working in a more challenging (high-priority) or less challenging (non-high-priority) school environment. We employed content analysis to analyze 64 suburban elementary school teachers' free-responses to a prompt regarding their stress as teachers. We cross-analyzed our findings through external auditing to bolster trustworthiness in the data and in the procedure. Findings: Teachers reported personal and contextual stressors. Herein, we reported concrete examples of the five categories of contextual stressors teachers identified: political and educational structures, instructional factors, student factors, parent and family factors, and school climate. We found directional qualities and overlapping relationships in the data, partially confirming our hypotheses. Implications for Research and Practice: We offer specific recommendations for practical ways in which school administrators might systemically address teacher stress based on the five categories of stressors reported by participants. We also suggest means of conducting action research to measure the effects of implemented suggestions.