An investigation of the anti-pronation effect of two taping methods after application and exercise

This study investigated the effect of two anti-pronation taping techniques on vertical navicular height, an indicator of foot pronation, after its application and 20 min of exercise. The taping techniques were: the low dye (LD) and low dye with the addition of calcaneal slings and reverse sixes (LDCR). A repeated measures study was used. It found that LDCR was superior to LD and control immediately after application and exercise. LD was better than control immediately after application but not after exercise. These findings provide practical directions to clinicians regularly using anti-pronation taping techniques.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.