People with amputation move asymmetrically with regard to kinematics (joint angles) and kinetics (joint forces and moments). Clinicians have traditionally sought to minimize kinematic asymmetries, assuming kinetic asymmetries would also be minimized. A cycling model evaluated locomotor asymmetries. Eight individuals with unilateral transtibial amputation pedaled with 172 mm-length crank arms on...

OBJECTIVES The limiting factors with regard to power output available for wheelchair ambulation have not been identified. The aim of the present study was to correlate power output during wheelchair driving with (i) power output and oxygen uptake during arm crank ergometry and (ii) arm muscle strength. METHODS Eleven disabled men were examined for maximal power output (POmax) during wheelchai...

Previous studies have sought to improve cycling performance by altering various aspects of the pedaling motion using novel crank-pedal mechanisms and non-circular chainrings. However, most designs have been based on empirical data and very few have provided significant improvements in cycling performance. The purpose of this study was to use a theoretical framework that included a detailed musc...

Abstract. We derive optimal order a posteriori error estimates for time discretizations by both the Crank–Nicolson and the Crank–Nicolson–Galerkin methods for linear and nonlinear parabolic equations. We examine both smooth and rough initial data. Our basic tool for deriving a posteriori estimates are second order Crank–Nicolson reconstructions of the piecewise linear approximate solutions. The...

The spark timing plays a significant role in the combustion process and in deciding the engine parameters of SI engine. This paper aims at demonstrating the effect of advanced and retarded spark timing on the burn fraction variation versus crank angle, cumulative heat release rate versus the crank angle and the pressure variation as a function of crank angle with the help of MATLAB programs. Fo...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...

We studied maximal torque-velocity relationships and fatigue during short-term maximal exercise on a constant velocity cycle ergometer in 13 healthy male subjects. Maximum torque showed an inverse linear relationship to crank velocity between 60 and 160 rpm, and a direct relationship to thigh muscle volume measured by computerized tomography. Peak torque per liter thigh muscle volume (PT, N X m...

have motivated much research. Here, p(n) denotes the number of partitions of n. In particular, toward a combinatorial explanation of the above congruences many partition statistics have been studied. Among them, the rank suggested by F. Dyson [6] and the crank suggested by the first author and F.G. Garvan [2] have proven successful and their own properties have been extensively studied. Here, t...

Abstract. A partition statistic ‘crank’ gives combinatorial interpretations for Ramanujan’s famous partition congruences. In this paper, we establish an asymptotic formula, Ramanujan type congruences, and q-series identities that the number of partitions with even crank Me(n) minus the number of partitions with odd crank Mo(n) satisfies. For example, we show that Me(5n + 4)− Mo(5n + 4) ≡ 0 (mod...

We utilize Dyson’s concept of the adjoint of a partition to derive an infinite family of new polynomial analogues of Euler’s Pentagonal Number Theorem. We streamline Dyson’s bijection relating partitions with crank ≤ k and those with k in the Rank-Set of partitions. Also, we extend Dyson’s adjoint of a partition to MacMahon’s “modular” partitions with modulus 2. This way we find a new combinato...