In this paper we study the preservation of Lyapunov functions in the numerical integration of ordinary differential equations. By means of a continuous extension and a projection technique we extend the technique proposed by Grimm and Quispel (BIT 45, 2005), so that it can be applied to other families Runge—Kutta methods such as the well known Dormand and Prince 5(4) pair. [ABSTRACT FROM AUTHOR]
The profiles of the edge of rectangular sheets of paper folded so as to join opposite edges were measured and compared with the profiles calculated with the theory of elasticity. I show how the calculation can be accomplished by using the aspect ratio of the loops as the only input parameter. [ABSTRACT FROM AUTHOR]