Influence of seat lumbar support adjustment on muscle fatigue under whole body vibration: An in vivo experimental study

BACKGROUND: In order to alleviate muscle fatigue and improve ride comfort, many published studies aimed to improve the seat environment or optimize seating posture. However, the effect of lumbar support on the lumbar muscle of seated subjects under whole body vibration is still unclear. OBJECTIVE: This study aimed to investigate the effect of lumbar support magnitude of the seat on lumbar muscle fatigue relief under whole body vibration. METHODS: Twenty healthy volunteers without low back pain participated in the experiment. By measuring surface electromyographic signals of erector spinae muscles under vibration or non-vibration for 30 minutes, the effect of different lumbar support conditions on muscle fatigue was analyzed. The magnitude of lumbar support d is assigned as d1= 0 mm, d2= 20 mm and d3= 40 mm for no support, small support and large support, respectively. RESULTS: The results showed that lumbar muscle activation levels vary under different support conditions. For the small support case (d2= 20 mm), the muscle activation level under vibration and no-vibration was the minimum, 42.3% and 77.7% of that under no support (d1= 0 mm). For all support conditions, the muscle activation level under vibration is higher than that under no-vibration. CONCLUSIONS: The results indicate that the small support yields the minimum muscle contraction (low muscle contraction intensity) under vibration, which is more helpful for relieving lumbar muscle fatigue than no support or large support cases. Therefore, an appropriate lumbar support of seats is necessary for alleviating lumbar muscle fatigue.

A computational framework for finding parameter sets associated with chaotic dynamics

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields

In the presence of the homogeneous electric field [Formula: see text] and the homogeneous perpendicular magnetic field [Formula: see text], the classical trajectory of a quantum particle on [Formula: see text] moves with drift velocity [Formula: see text] which is perpendicular to the electric and magnetic fields. For such Hamiltonians, the absence of the embedded eigenvalues of perturbed Hamiltonian has been conjectured. In this paper, one proves this conjecture for the perturbations [Formula: see text] which have sufficiently small support in the direction of drift velocity.

FINDING INVOLUTIONS WITH SMALL SUPPORT

We show that the proportion of permutations $g$ in $S_{\!n}$ or $A_{n}$ such that $g$ has even order and $g^{|g|/2}$ is an involution with support of cardinality at most $\lceil n^{{\it\varepsilon}}\rceil$ is at least a constant multiple of ${\it\varepsilon}$. Using this result, we obtain the same conclusion for elements in a classical group of natural dimension $n$ in odd characteristic that have even order and power up to an involution with $(-1)$-eigenspace of dimension at most $\lceil n^{{\it\varepsilon}}\rceil$ for a linear or unitary group, or $2\lceil \lfloor n/2\rfloor ^{{\it\varepsilon}}\rceil$ for a symplectic or orthogonal group.