PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.

Age-Related Differences in Coupling of Toe and Center of Pressure during the One-Legged Stance

This study aimed to investigate the characteristics of the coupling of the center of pressure (COP) movement and toes in older adults during one-legged standing (OLS). Participants were community dwelling older and younger adults. Toe vertical force during the OLS was recorded using a plantar-pressure distribution system, and the vertical forces in the hallux, little toe, and the first and fifth metatarsophalangeal (MP) joints were analyzed. A cross-correlation function was performed to examine the coordination between toes and between COP movement and four regions of the foot. The cross-correlation functions showed no significant difference in coefficients between toes. The OLS duration in the older adults was significantly correlated with the coefficient between the medial-lateral component of the COP and the first MP region. This study suggests that it is important to press the first MP region appropriately relative to COP movement to maintain the OLS.

D-CONVERGENCE OF ONE-LEG METHODS FOR STIFF DELAY DIFFERENTIAL EQUATIONS

Focuses on a study which explored the numerical solution of delay differential equations. Linear stability of numerical methods; Application of one-leg methods; Error analysis.

Convergence of one-leg methods for singular perturbation problems with delays

This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We obtain convergence results of A-stable one-leg methods with linear interpolation procedure. Numerical experiments further confirm our theoretical analysis.

Convergence of one-leg methods for nonlinear neutral delay integro-differential equations

Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper.

Convergence of Linear Multistep Methods and One-Leg Methods for Index-2 Differential-Algebraic Equations with a Variable Delay

Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.

Error of One-leg Methods for Singular Perturbation Problems with Delays

This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable one-leg methods with linear interpolation procedure.

Relationship between Respiratory Muscle Strength and Static Balance in Older People Requiring Support and Care

Purpose: This study aimed to clarify the relationship between respiratory muscle strength and balance in older people requiring support or nursing care. Methods: Thirty-seven older subjects aged 65 years or older who were certified as requiring nursing care or support were included in the study. Maximal inspiratory pressure (PIMAX), maximal expiratory pressure (PEMAX), and one-leg standing time were measured. Additionally, the Functional Reach Test (FRT) was performed. Pearson correlation coefficient and multiple regression analyses were performed. Results: One-leg standing time was positively correlated with PEMAX, and was particularly correlated with PIMAX, while FRT score was not correlated with respiratory muscle strength. Multiple regression analysis with one-leg standing time as the dependent variable and PIMAX and PEMAX as independent variables showed that only PIMAX was significantly correlated with one-leg standing time. Conclusion: Focusing on expiratory and inspiratory muscle strength is important for improving one-leg standing ability and thus preventing falls in older people.

Muscular activity patterns in 1-legged vs. 2-legged pedaling

Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle activation patterns between 2-legged and 1-legged pedaling.Methods:Fifteen healthy young recreational cyclists performed both 1-legged and 2-legged pedaling trials at about 30 Watt per leg.Surface electromyography electrodes were placed on 10 major muscles of the left leg.Linear envelope electromyography data were integrated to quantify muscle activities for each crank cycle quadrant to evaluate muscle activation changes.Results:Overall,the prescribed constant power requirements led to reduced downstroke crank torque and extension-related muscle activities(vastus lateralis,vastus medialis,and soleus)in 1-legged pedaling.Flexion-related muscle activities(biceps femoris long head,semitendinosus,lateral gastrocnemius,medial gastrocnemius,tensor fasciae latae,and tibialis anterior)in the upstroke phase increased to compensate for the absence of contralateral leg crank torque.During the upstroke,simultaneous increases were seen in the hamstrings and uni-articular knee extensors,and in the ankle plantarflexors and dorsiflexors.At the top of the crank cycle,greater hip flexor activity stabilized the pelvis.Conclusion:The observed changes in muscle activities are due to a variety of changes in mechanical aspects of the pedaling motion when pedaling with only 1 leg,including altered crank torque patterns without the contralateral leg,reduced pelvis stability,and increased knee and ankle stiffness during the upstroke.