Restrictions of the derivatives of positive real functions

Dissipative operators appear in abundance in the study of dynamical systems. In the classical circuit theory they are presented as Positive Real Functions. The coefficients of the Taylor expansion of PRF (driving-point impedance or admittance) must satisfy certain derived inequalities. A method is suggested for obtaining restrictions of the derivative of Positive Real Functions (Dissipative Operators).     

Teachers’ Use of Scaffolding Strategies During Read Alouds in the Preschool Classroom

Relatively little is known regarding preschool teachers’ use of specific scaffolds, including those high support scaffolds (e.g., co-participating, eliciting, reducing choices) that may be important for children who are struggling to acquire language and literacy concepts. The goal of this study was to characterize preschool teachers’ use of six types of scaffolds (generalizing, reasoning, predicting, co-participating, reducing choices, eliciting; see O’Connor et al. in Ladders to literacy, Paul H. Brookes Publishing, Baltimore, MD, 2005) within the whole group read aloud session. Two specific questions were addressed: (1) To what extent do preschool teachers use high and low support scaffolds during whole group read aloud sessions? and (2) To what extent does preschool teachers’ perceived frequency of use of specific scaffolds correspond to their actual use of scaffolds? Videotaped classroom observations were carried out for five preschool teachers conducting whole group read alouds in their classrooms; frequency of use for six types of scaffolds was coded using systematic observation procedures. Results indicated that teachers showed a preference for three types of scaffolds, all of which were low support, and that the three types of high support scaffolds occurred at very low rates. Additionally, results showed a substantial discrepancy between teachers’ perceived frequency of use of specific types of scaffolds relative to their actual use. Together, findings suggest that preschool teachers may benefit from professional development focused on using a range of scaffolds, to include high support scaffolds beneficial to children who may need high levels of support to participate in read alouds.     

Chronic flexibility gains: effect of isometric contraction duration during proprioceptive neuromuscular facilitation stretching techniques

The aim of this study was to assess the effect of to isometic contraction durations during propiceptive neuromuscular facilitation stretching on gains inflexion at the hip. Forty-three women (M age = 20.0 years, SD = 1.3) were assigned to one of three groups: 5-s isometric contraction (5-IC), 10-IC, and control. Flexibility was assessed at baseline and Weeks 3 and 6. Analysis of covariance, controlling for pretest differences, showed a significant interaction, F(2, 33) = 44.1, p < .001. Flexibility was significant lower in the control group relative to the 5-IC and 10-IC groups and in the 5-IC group relative to the 10-IC group at 3 and 6 weeks (3 weeks = 101.2 +/- 1.4 degrees, 114.3 +/- 1.5 degrees, 120.5 +/- 1.3 degrees; 6 weeks = 103.0 +/- 1.4 degrees, 126.1 +/- 1.6 degrees, 133.3 +/- 1.4 degrees for control, 5-IC and 10-IC groups, respectively). A longer contraction time led to greater increases in flexibility.