In his paper (1942), Ore found necessary and sufficient conditions under which the modular and distributive laws hold in the lattice of equivalence relations on a set S. In the present paper, we consider commuting equivalence relations. It has been proved by J6nsson (1953) that the modular law holds in the lattice of commuting equivalence relations. We give some necessary and sufficient conditi...

We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n−1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there...

Income status is an important variable that is strongly associated with certain commuting behaviours of workers. This paper presents new evidence on how polycentric development impacts on workers’ commuting behaviour among various income groups in Beijing, China. This study suggests that three key influencing factors—the public transport network, the location of affordable housing projects and ...

OBJECTIVE To investigate physical activity during leisure time and commuting among persons aged 15-69 years in the urban population of Tianjin, China, and to assess its associations with demographic and health-related characteristics. METHODS In 1996 a cross-sectional survey of 2002 males and 1974 females provided information on physical activity during leisure time and commuting and on demog...

We develop an equilibrium job search model in which employees incur commuting costs, and residential relocation is costly. We demonstrate that firms partially compensate workers for the incurred relocation costs to avoid paying compensation for commuting costs when house prices do not fully compensate the commuting costs. Taxing reimbursement of relocation costs at a higher rate than reimbursem...

The stressful characteristics of commuting constraints are conceptualized in terms of both physical and perceptual conditions of travel impedance. This study develops and operationalizes the concept of subjective impedance, as a complement to our previously developed concept of impedance as a physically defined condition of commuting stress. The stress impacts of high-impedance commuting were e...

Objective To investigate the association between active commuting and incident cardiovascular disease (CVD), cancer, and all cause mortality.Design Prospective population based study. Setting UK Biobank.Participants 263 450 participants (106 674 (52%) women; mean age 52.6), recruited from 22 sites across the UK. The exposure variable was the mode of transport used (walking, cycling, mixed mode ...

This paper, deals with some equivalence relations in fuzzy subgroups. Further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

BACKGROUND The current political agenda aims to promote active environments and physical activity while commuting to work, but research on it has provided mixed results. This study examines whether the proximity of green space and people's residence in different travel-related urban zones contributes to commuting physical activity. METHODS Population-based cross-sectional health examination s...