This cross-sectional study explored the extent and impact of mobile device-based Sleep Time-Related Information and Communication Technology (STRICT) use among American adolescents (N ¼ 3139, 49.3% female, mean age ¼ 13.3 years). Nearly 62% used STRICT after bedtime, 56.7% texted/tweeted/messaged in bed, and 20.8% awoke to texts. STRICT use was associated with insomnia, daytime sleepiness, eveningness, academic underperformance, later bedtimes and shorter sleep duration. Moderation analysis demonstrated that the association between STRICT use and insomnia increased with age, the association between STRICT use and daytime sleepiness decreased with age, and the association between STRICT use and shorter sleep duration decreased with age and was stronger in girls. Insomnia and daytime sleepiness partially mediated the relationship between STRICT use and academic underperformance. Our results illustrate the adverse interactions between adolescent STRICT use and sleep, with deleterious effects on daytime functioning. These worrisome findings suggest that placing reasonable limitations on adolescent STRICT use may be appropriate.

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It is well known that a function /: [0, 1]-» R is Baire 1 if and only if in any closed set C there is a point x0 at which the restricted function f\C is continuous. Functions will be called Baire* 1 if they satisfy the following stronger property: For every closed set C there is an open interval (a, b) with (a, b) n C =£ 0 such that f\C is continuous on (a, b). Functions which are both Baire* 1 and Darboux are examined. It is known that approximately derivable functions are Baire* 1. Among other things it is shown here that Lp-smooth functions are Baire* 1. A new result about the /_-differentiability of L^-smooth, Darboux functions is shown to follow immediately from the main properties of Baire* 1, Darboux functions.

It has recently been established that any Baire class one function f : [0, 1] → R can be represented as the pointwise limit of a sequence of polygonal functions whose vertices lie on the graph of f . Here we investigate the subclass of Baire class one functions having the additional property that for every dense subset D of [0, 1], the first coordinates of the vertices of the polygonal functions can be chosen from D.

In this paper we introduce a new form of differentiation for functions f: [0, 1]---R. This new form, while natural for Baire 1, Darboux functions, exhibits some surprising contrasts to the properties of established derivatives.Our derivates are defined by a process which we label selective. In this paper a process will be called selective if it has as its first step the selection of a fixed point from the interior of each closed non-degenerate subinterval of [0, 1]. Selective processes have been used to obtain characterizations of Baire 1, Darboux functions [10], derivatives [10], and, more recently, M3 functions [11].This paper consists of three sections. In the first, we give the necessary definitions and consider mainly the lower selective derivate. In this section we lay the foundations for most of the results of the second section. In the second section we show why selective differentiation is natural for Baire 1, Darboux functions and pass to a consideration of the finite selective derivative. At that time the similarities and contrasts between this derivative and the approximate derivative are shown. Finally, in the last section we look at the one-sided selective derivates and point out their fundamental pathology.