We consider several topics in the theory of partitions, focusing on questions regarding multipartitions. Results include the formulation of a combinatorial explanation of the crank statistic generalized to multipartitions; the conjecture and proof of several multipartition identities; the calculation of the number of k-partitions of n with crank n, n-1, or n-2; the construction of a crank-rever...

PURPOSE To determine the influence of arm-crank exercise in reproductive hormone levels in adults with chronic SCI. Further objectives were to assess the influence of arm-crank exercise on muscle strength and body composition. MATERIALS AND METHODS Seventeen male adults with complete SCI at or below the 5th thoracic level (T5) volunteered for this study. Participants were randomly allocated t...

in this study, a numerical model was developed to investigate the two-dimensional heat transfer in a homogenous finite cylinder to predict the local temperature and sterilizing value during caviar pasteurization. a fixed grid finite difference method was used in the solution of heat transfer equations according to crank-nicolson’s scheme. the model was validated by comparison of the experimenta...

and Applied Analysis 3 As in the classical Crank-Nicholson difference scheme, we will obtain a discrete approximation to the fractional derivative ∂U t, x /∂t at tn 1/2 , xi . Let H t, x 1 Γ 1 − α ∫ t 0 u s, x − u 0, x t − s α ds. 2.1

Abstract It is common practice within multi-body dynamic (MBD) modeling to assume that individual bodies are rigid however this can be an oversimplification especially when slender present resulting in inaccurate estimations of the system's natural frequencies and overall behavior. To address shortfall, we extend Udwadia–Kalaba (U–K) MBD formulation paper model flexible multibody systems for pu...

Bringmann and Dousse recently established a conjecture of Dyson dealing with the limiting asymptotics of the Andrews-Garvan crank statistic for integer partitions. A direct “sieving” technique is used to establish this conjecture and establish the range of validity. Unlike the approach of Bringmann and Dousse, the technique readily yields the analogous result for Dyson’s partition rank and all ...

Explicit, implicit–explicit and Crank–Nicolson implicit–explicit numerical schemes for solving the generalized lubrication equation are derived. We prove that the implicit– explicit and Crank–Nicolson implicit–explicit numerical schemes are unconditionally stable. Numerical solutions obtained from both schemes are compared. Initial curves with both zero and finite contact angles are considered....

Advection equations are an essential part of many mathematical models arising in different fields of science and engineering. It is important to treat such equations with efficient numerical schemes. The well-known Crank-Nicolson scheme will be applied. It will be shown that the accuracy of the calculated results can be improved when the Crank-Nicolson scheme is combined with the Richardson Ext...

In this paper, a numerical scheme named alternating segment Crank-Nikolson is used for solving heat equation. This scheme can be used directly on parallel computations. Truncation error and stability of the presented method is analyzed. Comparison in accuracy with the fully implicit Crank-Nikolson scheme is presented in numerical experiment.