Coefficients of Drinfeld modular forms and Hecke operators

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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.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

Public enterprise reforms and efficiency in regulated environments: the case of the postal sector

Purpose - This paper focuses on analyzing the effect that public reforms have on the efficiency of state-owned enterprises in regulated environments. Design/methodology/approach - The research is focused in the postal sector where public and private companies must obey a legal framework related to provide a universal service. The analysis is carried out using a panel of 7 European postal operators for the period 1997-2003. The activity analyzed was the letter mail division; we take as key variable the unit cost of a letter and use a translog cost function where as independent variables we include traffic levels, labor cost per employee, quality and availability of the service as well as the type of ownership (public or private). Additionally, in a second stage the geographical differences among countries are considered. Findings - Results indicate that postal operators that experienced organizational changes without being privatized, such as the Spanish and Greek operators, do not have higher unit costs than privatized postal operators like the one of Germany and the Netherlands. Moreover, we find that in all cases the operator of Ireland appear to be the most efficient. In this case restructuring process has been carried out giving an important leadership role to workers. This suggests us that labor culture could be a key variable to study when analyzing reform processes in public enterprises. Originality/value - Our findings show that in a regulated environment like in the postal sector, public and private companies can obtain similar efficiency levels in term of unit costs.

Innovation and Regulation in ICT. Keys for Development

The expansion of broadband speed and coverage over IP technology, which extend over transport and terminal access networks, has increased the demand for applications and content which by being provided over it, uniformly give rise to convergence. These shifts in technologies and enterprise business models are giving rise to the necessity for changing the perspective and scope of the Universal Service and of the regulation frameworks, with this last one based in the same principles as always but varying its application. Several aspects require special and renewed attention, such as the definition of relevant markets and dominant operators, the role of packages, interconnection of IP networks, network neutrality, the use of the spectrum with a vision of value for the citizenship, the application of the competition framework, new forms of licensing, treatment of the risk in the networks, changes in the regulatory authorities, amongst others. These matters are treated from the perspective of the actual trends in the world and its conceptual justification.

Impacte de les tecnologies de la informació i la comunicació en l’Administració de justícia: modernització i eficiència

L’Administració de Justícia, com servei públic que ha de donar als ciutadans una eficaç resolució dels conflictes, ha de comptar per al correcte compliment de la seva funció institucional, amb una sèrie de mitjans, no tan sols personals i materials, sinó també tecnològics, que li permetin assegurar la consecució de les seves finalitats. Per tant, es precisa una Administració oberta i transparent, caracteritzada per l’efectivitat i per la seva proximitat al ciutadà. La introducció de les TIC en l’Administració de Justícia és un procés bastant recent i encara no tancat, si es compara amb la resta del sector públic, especialment d’altres àmbits de l’Administració molt més avançats en la incorporació de les TIC, com són el tributari i el de la Seguretat Social. No obstant això, avui en dia, on majors èxits s’han assolit en aquest camp en l’Administració de Justícia és en el de la seva utilització interna: informatització interna, gestió interna dels procediments, intranets, etc. Per això, on queda un llarg camí per recórrer encara és en el camp de les relacions telemàtiques entre Administració de Justícia i els operadors jurídics, però especialment amb els ciutadans. D’altra banda, el legislador és sensible cada vegada més a aquest tema i s’ha preocupat de regular determinats aspectes on les TIC incideixen en l’àmbit de la justícia: actuacions dels procuradors, advocats, notificacions telemàtiques, el valor del document electrònic en el procés judicial... Així queda reflectit, per exemple, a la Llei Orgànica del Poder Judicial o la Llei d’Enjudiciament Civil. No obstant això, de lege ferenda, seria convenient l’existència d’un marc normatiu únic regulador de l’aplicació de les TIC en la Justícia. Així mateix, també ha d’assenyalar-se que en el procés institucional d’introducció de les noves tecnologies en la Justícia alguns dels acords adoptats així com les previsions contingudes en la normativa aplicable, no deixen de ser en la majoria dels casos simplement programàtics.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Maximal operators and differentiation theorems for sparse sets

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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.