consider the random walk among n places with n(n - 1)/2 transports. we attach an exponential random variable xij to each transport between places pi and pj and take these random variables mutually independent. if transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

BACKGROUND Few studies have assessed the predictors of changes in commuting. This study investigated the associations between physical environmental characteristics and changes in active commuting. METHODS Adults from the population-based European Prospective Investigation into Cancer (EPIC)-Norfolk cohort self-reported commuting patterns in 2000 and 2007. Active commuters were defined as tho...

We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint n× n matrices.

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis ...

We used participant-produced photography to investigate everyday commuting practices in Cambridge, UK. Photovoice served as an observational method for producing ethnographically rich data. A total of 19 participants produced over 500 photos about their journeys to and from work and took part in photo-elicitation interviews. Three themes emerged. First, many images depicted 'well-being' in comm...

At city level, personal monitoring is the best way to assess people's exposure. However, it is usually estimated from a few monitoring stations. Our aim was to determine the exposure to black carbon (BC) and BC dose for 45 schoolchildren with portable microaethalometers and to evaluate the relationship between personal monitoring and fixed stations at schools (indoor and outdoor) and in an urba...

In the paper one considers the local structure of the Fredholm joint spectrum of commuting n-tuples of operators. A connection between the spatial characteristics of operators and the algebraic invariant of the corresponding coherent sheaves is investigated. A notion of Weyl joint spectrum of commuting n-tuple is introduced.

‎In a recent paper C‎. ‎Miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{M}_n(mathbb{R})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎But the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎In this work we close the problem showing that also in this case the diameter is $4$.

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces provided that Hamilton–Jacobi equation Klein–Gordon–Fock a charged test particle can be integrated by the method complete separation variables are found. The is carried out using sets mutually commuting integrals motion type (1.1) whereby in privileged coordinate system, given equations turn into par...

BACKGROUND Active transportation has been associated with favorable health outcomes. Previous research highlighted the influence of neighborhood educational level on active transportation. However, little is known regarding the effect of commuting distance on social disparities in active commuting. In this regard, women have been poorly studied. The objective of this paper was to evaluate the r...