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In this paper we study Strichartz estimates for the half wave, the half Klein–Gordon and the Dirac Equations on compact manifolds without boundary, proving in particular for each of these flows local in time estimates both for the wave and Schrödinger admissible couples (in this latter case with an additional loss of regularity). The strategy for the proof is based on a refined version of the WKB approximation. [ABSTRACT FROM AUTHOR]

The aim of the present study was to analyse gender difference in morningnesseveningness preference by using the open questions of the Morningness-Eveningness Questionnaire. A sample of 1319 university students, age range 18 to 30 years, was administered the MEQ. A total of 240 (18.19%) morning-types, 795 (60.27%) intermediate-types, and 284 (21.53%) evening-types were identified. The men and women differed significantly in their mean scores (p < 0.00001) and distribution per circadian typology (p < 0.005), with the men presenting a more pronounced eveningness preference. The MEQ items referring to sleep onset phase were sensitive to gender differences irrespective of circadian typology. In contrast, the MEQ item regarding waking up time showed a significant crossover between gender and circadian typology, i.e., evening-men preferred waking up later than evening-women, but morning-men had a propensity to wake up earlier than morning-women. The results seem to support the hypothesis that the circadian system is more flexible in men than in women. [ABSTRACT FROM AUTHOR]