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).     

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.     

THE CELTIC LANGUAGES AND TELEVISION

The article proposes the subtitling of English television programmes in the Celtic languages and of Celtic language programmes in English in order to serve the Celtic speaking minorities in Britain and to produce an appreciation of the Celtic languages among English speaking viewers. Parallels are drawn between the proposed British bilingual project and those in other countries for deaf viewers and for speakers of minority languages. Results of a survey of English and Welsh viewers are reported, and difficulties such as viewer resistance, cost, etc., of implementing a bilingual subtitling program in Britain are discussed.