We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and set behave like compact set. demonstrate uniform continuity Arzela-Ascoli-type theorem. propose notion special submanifolds with tubular neighborhoods show that any is decomposed into finitely many neighborhoods.

background : we need a defined population for determining prevalence and incidence of diseases, as well as conducting interventional, cohort and longitudinal studies, calculating correct and timely public health indicators, assessing actual health needs of community, performing educational programs and interventions to promote healthy lifestyle, and enhancing quality of primary health services....

Abstract. A certain subclass of analytic functions in the open unit disc with negative coefficients is introduced. The new class is defined by means of multiplier transformations. By making use of the familiar concept of neighborhoods of analytic function, the author proves coefficient inequalities, distortion theorems and associated inclusion relations for the (n, δ)-neighborhoods of functions...

The literature on neighborhood effects on schooling theorizes that neighborhood cultural context is an important mechanism generating such effects. However, explanations that rely on subcultural theories, such as oppositional culture, have met with considerable criticism on empirical grounds, and no alternative account of the cultural context of disadvantaged neighborhoods has been developed in...

Diversity of neighborhood amenities may promote the mobility of older adults. A 2010 community-based sample of 510 adults aged ≥65 years in Philadelphia, Pennsylvania, and geospatial data from the Esri Business Analyst database (Esri, Inc., Redlands, California) were used to assess associations of neighborhood amenity diversity with mobility. Neighborhoods were defined by census tract, and dive...

An “odd-rule” cellular automaton (CA) is defined by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF. We classify all the odd-rule CAs defined by neighborhoods which are subsets of a 3× 3 grid of square cells. There are 86 different CAs modulo trivial symmetri...