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....

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.

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 ...

This paper proposes a modified non-dominated sorting genetic algorithm (NSGA-II) for a bi-objective location-allocation model. The purpose is to define the best places and capacity of the distribution centers as well as to allocate consumers, in such a way that uncertain consumers demands are satisfied. The objectives of the mixed-integer non-linear programming (MINLP) model are to (1) minimize...

in this article, we apply the multiquadric radial basis function (rbf) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the kawahara equation. the scheme is based on the crank-nicolsonformulation for space derivative. the performance of the method is shown innumerical examples.

system evaluations were performed on 48 center pivots in different parts of saudi arabia. these systems, located on different farms in four different regions of the country, namely: riyadh, jouf, qassim and eastern regions, were evaluated to study the effect of lateral configuration on water application uniformity as regards the original vs. modified laterals. lateral configuration modification...

T he achievement of Karl Mahlburg in this issue of PNAS (1) adds a lustrous chapter to a unique mathematical object: the crank. In 1944, the crank was first hinted at by Freeman Dyson (2), then an undergraduate at Cambridge University. He had written an article, titled Some Guesses in the Theory of Partitions, for Eureka, the undergraduate mathematics journal of Cambridge. Dyson discovered the ...

This paper describes a method for defining the maximum torque which can be produced at a joint from isovelocity torque measurements on an individual. The method is applied to an elite male gymnast in order to calculate subject specific joint torque parameters for the knee joint. Isovelocity knee extension torque data were collected for the gymnast using a two repetition concentric-eccentric pro...