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...

nowadays, due to the increasing power of diesel engines, especially heavy duty diesel engines, and increasing gas pressure inside the combustion chamber, the forces acting on the engine bearings have dramatically raised. on the other hand, becaus eof the competition in the market, it is necessary to increase the engine bearing life and reduce its failure as much as possible. the engine bearings...

phenol is a common pollutant that was listed by us environmental protection agency (epa) among the priority pollutants. classical methods employed for phenol removal are either costly or limited to large-scale applications such as biological and thermal decomposition methods. in this study, adsorption of phenol by a type of clay that is extracted from a local soil called khoweldi was investigat...

The aim of this study was to evaluate the impact of a novel crank system on laboratory time-trial cycling performance. The Rotor system makes each pedal independent from the other so that the cranks are no longer fixed at 180°. Twelve male competitive but non-elite cyclists (mean ± s: 35 ± 7 yr, Wmax = 363 ± 38 W, VO2peak = 4.5 ± 0.3 L·min(-1)) completed 6-weeks of their normal training using e...

An implicit energy-decaying modified Crank--Nicolson time-stepping method is constructed for the viscous rotating shallow water equation on plane. Existence, uniqueness, and convergence of semidiscrete solutions are proved by using Schaefer's fixed point theorem $H^2$ estimates discretized hyperbolic--parabolic system. For practical computation, further in space, resulting a fully discrete fini...