An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Isokinetic muscle strength and knee function associated with double femoral pin fixation and fixation with interference screw in anterior cruciate ligament reconstruction

Intensive scheduling in sports requires athletes to resume physical activity shortly after injury. The purpose of this study was to investigate early isokinetic muscle strength and knee function on bone-patellar tendon-bone (BPTB) ACL reconstruction with double femoral pin fixation or interference screw technique. A prospective study was conducted from 2008 to 2009, with 48 athletes who received femoral BPTB fixation with interference screw (n = 26) or double pin (n = 22). Clinical (IKDC objective score and hop test) and isokinetic muscle strength (peak torque (PT), PT/body weight and flexion/extension rate (F/E) in 60 and 240A degrees/s) were analyzed at 6 months of follow-up. Analysis at baseline showed no differences between groups before surgery related to age, gender, associated injury, Tegner or Lysholm score; thus showing that groups were similar. During follow-up, however, there were significant differences between the two groups in some of the isokinetic muscle strength: PT/BW 60A degrees/s (Double Pin = 200% +/- A 13% vs. Interference Screw = 253% +/- A 16%*, *P = 0.01); F/E 60A degrees/s (Double Pin = 89% +/- A 29%* vs. Interference Screw = 74% +/- A 12%, *P = 0.04). No statistical differences between groups were observed on IKDC objective score, hop test and complications. The significant muscle strength outcome of the interference screw group found in this study gives initial evidence that this fixation technique is useful for athletes that may need accelerated rehabilitation. Early return to sports ability signaled by isokinetic muscle strength is of clinical relevance as it is one of the main goals for athletes' rehabilitation. III.

Trans-Planckian problem in the healthy extension of Horava-Lifshitz gravity

Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasiexponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The Horava-Lifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the trans-Planckian region the fluctuations obey a nonlinear dispersion relation of Corley-Jacobson type. In the "healthy extension" of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wave number with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wave number. Taking the usual inflationary parameters we find that the frequency of the oscillations is so large as to render the effect difficult to observe.

Influence of high-heeled shoes on venous function in young women

Background: Walking with high-heeled shoes is a common cause of venous complaints such as pain, fatigue, and heavy-feeling legs. The aim of the study was to clarify the influence of high-heeled shoes on the venous return and test the hypothesis that women wearing different styles of high-heeled shoes present an impaired venous return when compared with their values when they are barefoot. Methods: Thirty asymptomatic women (mean age, 26.4 years) wearing appropriately sized shoes were evaluated by air plethysmography (APG), a test that measures changes in air volume on a cuff placed on the calf, while they performed orthostatic flexion and extension foot movements and altered standing up and lying down. The test was repeated in four situations: barefoot (0 cm), medium heels (3.5 cm), stiletto high heels (7 cm), and platform high heels (7 cm). The APG values of venous filling index (VFI), ejection fraction (EF), and residual volume fraction (RVF) were divided into four groups according to heel height and compared by repeated-measures analysis of variance. Results: RVF was increased in the groups wearing high heels (stiletto and platform) compared with the barefoot group (P < .05). RVF was increased in the medium-heel group (3.5 cm) compared with the barefoot group (P < .05), and despite the lack of statistical significance, the medium-heel group showed lower values of RVF compared with the two high-heel groups. The EF parameter followed the opposite tendency, showing higher values for the barefoot group compared with the other three groups (P < .05). Values for VFI were similar in the three situations evaluated. Conclusions: High heels reduce muscle pump function, as demonstrated by reduced EF and increased RVF values. The continuous use of high heels tends to provoke venous hypertension in the lower limbs and may represent a causal factor of venous disease symptoms. (J Vasc Surg 2012;56:1039-44.)