Normality in terms of distances and contractions

The main purpose of this paper is to explore normality in terms of distances between points and sets. We prove some important consequences on realvalued contractions, i.e. functions not enlarging the distance, showing that as in the classical context of closures and continuous maps, normality in terms of distances based on an appropriate numerical notion of $\gamma$-separation of sets, has far reaching consequences on real valued contractive maps, where the real line is endowed with the Euclidean metric. We show that normality is equivalent to (1) separation of $\gamma$-separated sets by some Urysohn contractive map, (2) to Kat\v{e}tov-Tong's interpolation, stating that for bounded positive realvalued functions, between an upper and a larger lower regular function, there exists a contractive interpolating map and (3) to Tietze's extension theorem stating that certain contractions defined on a subspace can be contractively extended to the whole space. The appropriate setting for these investigations is the category of approach spaces, but the results have (quasi)-metric counterparts in terms of non-expansive maps. Moreover when restricted to topological spaces, classical normality and its equivalence to separation by a Urysohn continuous map, to Kat\v{e}tov-Tong's interpolation for semicontinuous maps and to Tietze's extension theorem for continuous maps are recovered

How Many Closed Structures does the Construct PRAP Admit?

We will prove that the topological construct PRAP, introduced by E. and R. Lowen in [9] as a numerification supercategory of the construct PRTOP of convergence spaces and continuous maps, admits a proper class of monoidal closed structures. We will even show that under the assumption that there does not exist a proper class of measurable cardinals, it admits a proper conglomerate (i.e. one which is not codable by a class) of mutually non-isomorphic monoidal closed structures. This severely contrasts with the situation concerning symmetric monoidal closed structures, because it is shown in [13] that PRAP only admits one symmetric tensorproduct, up to natural isomorphism

The influence of parenting style on health related behavior of children : findings from the ChiBS study

Objective: Exploring associations between parenting behavior and children's health related behavior including physical activity, sedentary behavior, diet and sleep. Methods: We recruited 288 parents and their children (6-12y old). Children's weight and height were measured. Fat percentage was determined by air displacement plethysmography. Parents reported socio-demographic data, sleep information, physical activity and sedentary behavior of their child and completed the Comprehensive General Parenting Questionnaire (CGPQ) and a Food Frequency Questionnaire. Children completed the Dutch Eating Behavior Questionnaire. Associations between parenting behavior (CGPQ) and children's health related behavior were assessed with univariate and multiple regression analyses. Results: A small positive correlation was found between sweet food consumption frequency and "coercive control" (r = 0.139) and a small negative correlation between fruit and vegetables consumption frequency and "overprotection" (r = -0.151). Children consumed more frequently soft drinks when their parents scored lower on "structure" (r = -0.124) and higher on "overprotection" (r = 0.123); for the light soft drinks separately, a small positive correlation with "behavioral control" was found (r = 0.172). A small negative correlation was found between "emotional eating" and "structure" (r = -0.172) as well as "behavioral control" (r = -0.166). "Coercive control" was negatively correlated with the child's sleep duration (r = -0.171). After correction for confounding factors, the following significant associations were found: (1) a small negative association between "structure" and soft drinks consumption (beta = -0.17 for all soft drinks and -0.22 for light soft drinks), (2) a small positive association between "behavioral control" and light soft drinks (beta = 0.34), (3) a small positive association of "nurturance" and "coercive control" with sedentary behavior (beta = 0.16 for both parent constructs) and (4) a small negative association between the parenting construct "coercive control" and sleep duration (beta = -0.23). Conclusion: The significant but small associations between parenting constructs and the investigated variables suggest that different aspects of parenting style play an important role in the genesis of the health related behavior of children. Overall, our findings suggest that health professionals should encourage parents to apply the more positive parenting constructs i.e., more "structure" and "behavioral control", and less "coercive control". They could, for instance, supervise and manage their child's activities and help their child to achieve certain goals

Ring ideals and the Stone-Čech compactification in pointfree topology

AbstractThis paper shows that the compact completely regular coreflection in the category of frames is given by the frame of Jacobson radical ideals of the ring RL of real-valued continuous functions on L, as an alternative to its familiar representations in terms of (i) the l-ideals of RL as lattice-ordered ring or (ii) the ideals of the bounded part of RL which are closed in the usual uniform topology. Further, in analogy with this, the compact zero-dimensional coreflection will also be described in terms of ring ideals, this time of the ring ZL of integer-valued continuous functions on L

Weak representations of quantified hyperspace structures

AbstractIt is the aim of this note, to show that several results from Beer (1993), Beer et al. (1992) and Beer and Lucchetti (1993) about the description of some hypertopologies as weak or initial topologies can be generalized to the quantitative setting of approach hyperspace structures as introduced by Lowen and Sioen (1996, 1998)

Does home cooking have an effect on phthalate levels in food?

A

Locally convex approach spaces

[EN] We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.Sioen, M.; Verwulgen, S. (2003). Locally convex approach spaces. Applied General Topology. 4(2):263-279. doi:10.4995/agt.2003.2031.SWORD2632794

Fat tissue accretion in children and adolescents : interplay between food responsiveness, gender, and the home availability of snacks

The appetitive trait "food responsiveness" is assumed to be a risk factor for adiposity gain primarily in obesogenic environments. So far, the reported results are inconsistent in school-aged children, possibly because these studies did not take into account important moderators such as gender and the food-environment. In order to better inform caregivers, clinicians and the developers of targeted obesity-prevention interventions on the conditions in which food responsiveness precedes adiposity gain, the current study investigated if this relationship is stronger in girls and in children exposed to a higher home availability of energy-dense snacks. Age- and sex-independent Fat and Lean Mass Index z-scores were computed based on air-displacement plethysmography at baseline and after 2 years in a community sample of 129 children (48.8% boys) aged 7.5-14 years at baseline. Parents reported at baseline on children's food responsiveness and the home availability of energy-dense snacks. Food responsiveness was a significant predictor of increases in Fat Mass Index z-scores over 2 years in girls but not boys. The home availability of energy-dense snacks did not significantly moderate the relation of food responsiveness with Fat Mass Index z-score changes. The results suggest that food responsiveness precedes accelerated fat tissue accretion in girls, and may inform targeted obesity-prevention interventions. Further, future research should investigate to which food-environmental parameters children high in food responsiveness mainly respond

Children’s body composition and stress, the ChiBS study : aims, design, methods, population and participation characteristics

BACKGROUND: The last decades, the prevalence of childhood obesity has increased. Apart from other lifestyle factors, the effect of chronic psychosocial stress on the development of obesity has been recognized. However, more research is needed into the influence of chronic stress on appetite regulation, energy balance and body composition, as well as on the interaction with physical activity/sedentary behavior, diet and sleep in children. In this regard, the ChiBS study (Children’s Body composition and Stress) was designed at the Ghent University. Within this paper, we describe the aims, design, methods, participation and population characteristics of the ChiBS study. METHODS: The influence of chronic stress on changes in body composition is investigated over a two-year follow-up period (February-June 2010, 2011 and 2012) in primary-school children between 6 and 12 years old in the city Aalter (Flanders, Belgium). Stress is measured by child- and parent-reported stress-questionnaires, as well as by objective stress biomarkers (serum, salivary and hair cortisol) and heart rate variability. Body composition is evaluated using basic anthropometric measurements and air displacement plethysmography. Additional information on socio-economic status, medical history, physical activity, dietary intake and sleep are obtained by questionnaires, and physical activity by accelerometers. RESULTS: The participation percentage was 68.7% (N = 523/761), with 71.3% of the children willing to participate in the first follow-up survey. Drop-out proportions were highest for serum sampling (12.1%), salivary sampling (8.3%) and heart rate variability measurements (7.4%). DISCUSSION: The ChiBS project is unique in its setting: its standardized and longitudinal approach provides valuable data and new insights into the relationship between stress and changes in body composition in a large cohort of young children. In addition, this study allows an in-depth investigation of the validity of the different methods that were used to assess stress levels in children