We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gradients. Integrators which exactly conserve all the first integrals simultaneously are then defined. In both cases we start from an arbitrary method of a prescribed order (say, a Runge-Kutta scheme) and modify it using two approaches: one based on projection and one based one local coordinates. The methods are tested on the Kepler problem.

No abstract

Social networks in the community are essential for solving problems caused by the aging society. We showed the possible applications of face-to-face interactional data for identifying core participants having many interactions, and isolated participants having only a few interactions within the community. Such data would be useful for carrying out efficient interventions for increasing participants' involvement with their community. Geriatr Gerontol Int 2017; 17: 1752-1758.

No abstract

No abstract