In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting.

In this paper, Crank-Nicholson method for solving fractional wave equation is considered. The stability and consistency of the method are discussed by means of Greschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions.

The aim of our study was to compare crank torque profile and perceived exertion between the Monark ergometer (818 E) and two outdoor cycling conditions: level ground and uphill road cycling. Seven male cyclists performed seven tests in seated position at different pedaling cadences: (a) in the laboratory at 60, 80, and 100 rpm; (b) on level terrain at 80 and 100 rpm; and (c) on uphill terrain (...

A CRANK has been defined, probably by Bernard Shaw, champion of all cranks, as a person who holds and acts upon an opinion that is contrary to orthodox teaching, but it is claimed directly he has converted a sufficiently large number of his fellows to his point of view he ceases to be a crank. This is seldom true, as all worthy cranks have more than one arrow in their quiver. They have made the...

PURPOSE The aim of this study was to compare asynchronous (ASY) arm cranking (cranks at 180° relative to each other) with synchronous (SYN) arm cranking (parallel crank setting) during the 30 s Wingate anaerobic test. METHODS Thirty two physically active men (aged 22.1 ± 2.4 y) completed two Wingate tests (one ASY and one SYN) separated by 4 d in a randomized counterbalanced order. The Wingat...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

The oscillating activity of a single CDK-cyclin fusion protein can drive the orderly progression of yeast cells through DNA replication, mitosis and cell division.