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.

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 ...

nonspecific activity-related arm pain is characterized by an absence of objective physical findings and symptoms that do not correspond with objective pathophysiology. arm pain without strict diagnosis is often related to activity, work-related activity in particular, and is often seen in patients with physically demanding work. psychological factors such as catastrophic thinking, symptoms of d...

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...

Let N(≤ m,n) denote the number of partitions of n with rank not greater than m, and let M(≤ m,n) denote the number of partitions of n with crank not greater than m. Bringmann and Mahlburg observed that N(≤ m,n) ≤ M(≤ m,n) ≤ N(≤ m + 1, n) for m < 0 and 1 ≤ n ≤ 100. They also pointed out that these inequalities can be restated as the existence of a re-ordering τn on the set of partitions of n suc...

BACKGROUND The reported accuracy of clinical tests for superior labral anterior posterior lesions is extremely variable. Pooling results from multiple studies of higher quality is necessary to establish the best clinical tests to use. HYPOTHESIS Certain clinical tests are superior to others for diagnosing the presence or absence of a superior labral anterior posterior lesion. STUDY DESIGN M...

Andrews’ spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank and rank moment functions. This implies an inequality between crank and rank moments that was only known previously for sufficiently large n and...

In this paper we present a posteriori error estimators for the approximate solutions of linear parabolic equations. We consider discretizations of the problem by discontinuous Galerkin method in time corresponding to variant Crank-Nicolson schemes and continuous Galerkin method in space. Especially, £nite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson...