Adopting the point-neighbourhood definition of topology, which we think may in some cases help acquire a very good insight of digital topologies, we unify the proof technique of the results on 4-connectedness and on 8-connectedness in Z . We also show that there is no topology compatible with 6-connectedness. We shortly comment on potential further use of this approach.

BACKGROUND Few studies have considered the joint effects of social and physical environments on physical activity (PA). The primary purpose of this study was to examine the compounding effects of neighbourhood walkability and social connectedness on PA. METHODS Data were collected from adults (n = 380) in Waterloo, Ontario, Canada. Perceptions of neighbourhood social connectedness and walkabi...

This paper attempts to provide a systematic view to the λ-connectedness method. This method is for classification/segmentation, fitting/reconstruction, and inference. A common type of partial connectivity that describes the phenomenal of gradual variation is studied in various domains. The previous research work on λ-connectedness was abstracted and integrated into a unified framework: a networ...

Adolescent suicide is a major public health concern. Stressing the need for public health-based solutions, the Centers for Disease Control and Prevention identified "connectedness" as one means of pursuing this agenda. To advance this effort in suicide prevention with adolescents, (1) consistencies and variation in the literature overtly linking connectedness to suicide thoughts and behaviors (...

The Yoccoz puzzle is a fundamental tool in Holomorphic Dynamics. The original combinatorial argument by Yoccoz, based on the BrannerHubbard tableau, counts the preimages of a non-degenerate annulus in the puzzle. However, in some important new applications of the puzzle (notably, matings of quadratic polynomials) there is no non-degenerate annulus. We develop a general combinatorial argument to...

Many public goods that are provided by coalitions have a group-size e¤ect. Namely, people prefer to consume a public good in a larger coalition. This paper studies local public goods games with anonymous and separable group-size e¤ect. The core is nonempty when coalition feasible sets are monotonic and players’preferences over public goods satisfy a condition called cardinal connectedness. More...

As a fairly new establishment for childcare, afterschool programs are understudied. However, some research proposes that these environments provide risk prevention for problem behavior. This research investigates the roles of attendance and connectedness in afterschool programs upon children's substance abuse and problem behavior. Multiple regression analysis was used among 22 programs to gauge...

in this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.