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.

Hankel operators on holomorphic Hardy-Orlicz spaces

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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.

Chaos and order in the contemporary city. The impact of urban spatial structure on population density and commuting distance in Barcelona, 1986-2001.

One of the criticisms leveled at the model of dispersed city found all over the world is its unarticulated, random, and undifferentiated nature. To check this idea in the Barcelona Metropolitan Region, we estimated the impact of the urban spatial structure (CBD, subcenters and transportation infrastructures) over the population density and commuting distance. The results are unfavorable to the hypothesis of the increasing destructuring of cities given that the explanatory capacity of both functions improves over time, both when other control variables are not included and when they are included.

Iowa Commuting Patterns, 2000

A century ago, the majority of workers were employed near their homes—on farms or in cities and towns. As industrialization increased and suburbs surrounded central cities, commuting meant going from homes in suburbs to jobs in cities. Today, there is a growing trend of workers commuting between suburbs. On any given day, 61,775 workers commute to jobs in Iowa counties other than the one in which they live. The most important reason for increased commuting has been employment growth. Rising incomes and the growth of suburbs have also been factors. In the past, the increased employment of women added to the number of commuters. Commuting patterns are a key consideration in transportation planning. In more urban states than Iowa, there is concern that the use of mass transit continues to decline. In Iowa, where so much of our commuting is between counties, private vehicles are often the only practical means of getting to and from work. On any given day, 1,155,008 single-occupancy vehicles are driven to and from jobs somewhere in Iowa. At the same time, an additional158,699 workers share rides by participating in carpools.

Longitudinal and cross-sectional changes in active commuting to school among Brazilian schoolchildren.

OBJECTIVE: The objective of the study is to evaluate cross-sectional and longitudinal changes in children's commuting to school in a representative sample of a Brazilian city. METHODS: Two school-based studies were carried out in 2002 (n=2936; 7-10years old) and 2007 (n=1232; 7-15years old) in Florianopolis, Brazil. Cross-sectional data were collected from children aged 7 to 10years in 2002 and 2007. Longitudinal analyses were performed with data from 733 children participating in both surveys. Children self-reported their mode of transportation to school using a validated illustrated questionnaire. Changes were tested with chi square statistics and McNemar's test. RESULTS: Cross-sectional data showed a 17% decline in active commuting; a decrease from 49% in 2002 to 41% in 2007. On the other hand, active commuting among the 733 children increased as they entered adolescence 5years later, rising from 40% to 49%. CONCLUSION: Active commuting to school decreased in Brazilian children aged 7-10years over a five year period; whereas, it increased among children entering adolescence. Policies should focus on safety and environmental determinants to increase active commuting.

Safe Bicycling in Iowa, May 7, 2001

Bicycling, once considered a recreational activity for the young, has suddenly become a popular means of transportation for adults. The recent rise in fuel costs, an increased interest in physical fitness and concern for the environment have resulted in a growing number of adults choosing to commute by bike. The benefits of commuting by bicycle are numerous, and include saving money, promoting good health and energy conservation. However, the combination of bicycles and motor vehicles on public roads is not always a pleasant experience. Increasing numbers of cyclists on city streets lead to increased conflicts with motor vehicles and can endanger both vehicle operators.

Are commuting and residential mobility decisions simultaneous? : the case of Catalonia (Spain)

In this paper we study the commuting and moving decisions of workers in Catalonia (Spain) and its evolution in the 1986-1996 period. Using a microdata sample from the 1991 Spanish Population Census, we estimate a simultaneous, discrete choice model of commuting and moves, thus indirectly addressing the home and job location decisions. The econometrical framework is a simultaneous, binary probit model with a commute equation and a move equation

A territorial model of commuting in Catalonia, 1986-1996

Commuting consists in the fact that an important fraction of workers in developed countries do not reside close to their workplaces but at long distances from them, so they have to travel to their jobs and then back home daily. Although most workers hold a job in the same municipality where they live or in a neighbouring one, an important fraction of workers face long daily trips to get to their workplace and then back home.Even if we divide Catalonia (Spain) in small aggregations of municipalities, trying to make them as close to local labour markets as possible, we will find out that some of them have a positive commuting balance, attracting many workers from other areas and providing local jobs for almost all their resident workers. On the other side, other zones seem to be mostly residential, so an important fraction of their resident workers hold jobs in different local labour markets. Which variables influence an area¿s role as an attraction pole or a residential zone? In previous papers (Artís et al, 1998a, 2000; Romaní, 1999) we have brought out the main individual variables that influence commuting by analysing a sample of Catalan workers and their commuting decisions. In this paper we perform an analysis of the territorial variables that influence commuting, using data for aggregate commuting flows in Catalonia from the 1991 and 1996 Spanish Population Censuses.These variables influence commuting in two different ways: a zone with a dense, welldeveloped economical structure will have a high density of jobs. Work demand cannot be fulfilled with resident workers, so it spills over local boundaries. On the other side, this economical activity has a series of side-effects like pollution, congestion or high land prices which make these areas less desirable to live in. Workers who can afford it may prefer to live in less populated, less congested zones, where they can find cheaper land, larger homes and a better quality of life. The penalty of this decision is an increased commuting time. Our aim in this paper is to highlight the influence of local economical structure and amenities endowment in the workplace-residence location decision. A place-to-place logit commuting models is estimated for 1991 and 1996 in order to find the economical and amenities variables with higher influence in commuting decisions. From these models, we can outline a first approximation to the evolution of these variables in the 1986-1996 period. Data have been obtained from aggregate flow travel-matrix from the 1986, 1991 and 1996 Spanish Population Censuses