Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Heterogeneity assumptions in the specification of bargaining models: a study of household level trade-offs between commuting time and salary

With many real world decisions being made in conjunction with other decision makers, or single agent decisions having an influence on other members of the decision maker's immediate entourage, there is strong interest in studying the relative weight assigned to different agents in such contexts. In the present paper, we focus on the case of one member of a two person household being asked to make choices affecting the travel time and salary of both members. We highlight the presence of significant heterogeneity across individuals not just in their underlying sensitivities, but also in the relative weight they assign to their partner, and show how this weight varies across attributes. This is in contrast to existing work which uses weights assigned to individual agents at the level of the overall utility rather than for individual attributes. We also show clear evidence of a risk of confounding between heterogeneity in marginal sensitivities and heterogeneity in the weights assigned to each member. We show how this can lead to misleading model results, and argue that this may also explain past results showing bargaining or weight parameters outside the usual [0,1] range in more traditional joint decision making contexts. In terms of substantive results, we find that male respondents place more weight on their partner's travel time, while female respondents place more weight on their partner's salary.

Choice of commuting mode among employees: Do home neighborhood environment, worksite neighborhood environment, and worksite policy and supports matter?

BACKGROUND: Promoting the use of public transit and active transport (walking and cycling) instead of car driving is an appealing strategy to increase overall physical activity.

PURPOSE: To quantify the combined associations between self-reported home and worksite neighborhood environments, worksite support and policies, and employees' commuting modes.

METHOD: Between 2012 and 2013, participants residing in four Missouri metropolitan areas were interviewed via telephone (n = 1,338) and provided information on socio-demographic characteristics, home and worksite neighborhoods, and worksite support and policies. Commuting mode was self-reported and categorized into car driving, public transit, and active commuting. Commuting distance was calculated using geographic information systems. Commuters providing completed data were included in the analysis. Multivariate logistic regression models were used to examine the correlates of using public transit and active commuting.

RESULT: The majority of participants reported commuting by driving (88.9%); only 4.9% used public transit and 6.2% used active modes. After multivariate adjustment, having transit stops within 10-15 minutes walking distance from home (p=0.05) and using worksite incentive for public transit (p<0.001) were associated with commuting by public transit. Commuting distance (p<0.001) was negatively associated with active commuting. Having free or low cost recreation facilities around the worksite (p=0.04) and using bike facilities to lock bikes at the worksite (p<0.001) were associated with active commuting.

CONCLUSION: Both environment features and worksite supports and policies are associated with the choice of commuting mode. Future studies should use longitudinal designs to investigate the potential of promoting alternative commuting modes through worksite efforts that support sustainable commuting behaviors as well as the potential of built environment improvements.

Determinants of uptake and maintenance of active commuting to school

The objective was to identify determinants of uptake and maintenance of active school travel (AST) over 4 years in children aged 9 at baseline. Data from wave 1 (n=8502) and 2 (n=7479) of the Growing Up in Ireland study were analysed. At 9- and 13-years 25% and 20% engaged in AST. Children were more likely to maintain or take-up AST if they lived in an urban area. Change in distance to school influenced both maintenance and adoption of AST, with a negative impact seen for increased distance between 9 and 13 years and a positive impact seen for decreased distance. Some factors which predict uptake and maintenance of AST are modifiable and can inform intervention development.

Tensor products of operator systems

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C*-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C*-algebra yet has the property that for every C*-algebra A, the minimal and maximal tensor product of S and A are equal.

Long hours in paid and domestic work and subsequent sickness absence: does control over daily working hours matter?

Objectives: To explore the associations of working hours ( paid, domestic, commuting, and total) with sickness absence, and to examine whether these associations vary according to the level of employee control over daily working hours.

The social consequences of broken urban structures: a case study of Belfast

This article explores how the design and layout of the urban environment can have significant social impacts on working class communities whose access to employment and other necessary services depends largely on public transport and safe walk-able streets. It does so by considering a case study of Belfast. Although Belfast has a distinctive recent history as the site of political violence and territorial division, it also has a spatial configuration that emerged out of a modernising roads and redevelopment programme in the 1960s and 1970s. However, an understanding of contemporary Belfast, particularly its urban structure and form, requires n analysis of how the social impacts of such ubiquitous regional and urban planning practices were not addressed. The article argues that a culture of ‘politically safe’ bureaucratic inaction developed during the ‘war years’ has been sustained in the ‘new democracy’. In turn, this has had significant consequences for the functioning of the city. Major areas of derelict land around the city core together with the impediments created by regional road infrastructure have combined to create a doughnut city that, on the one hand, facilitates a commuting middle class, while on the other, discriminates against the poorest inner city communities. The article goes on to examine how an activist urban design group, known as the Forum for Alternative Belfast, has responded to these challenges. It focuses particularly on action-research undertaken during its 2010 Summer School which aimed to address issues of disconnection in inner North Belfast that affect some of the most territorialised and deprived communities in the city.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.