Positively invariant sets play an important role in the theory and
applications of dynamical systems. The stability in the sense of
Lyapunov of the equilibrium x = 0 is equivalent to the existence of the
ellipsoidal positively invariant sets. The constraints on the state and
control vectors of dynamical systems can be formulated as polyhedral
positively invariant sets in practical engineering problems. Numerical
checking method of positive invariance of polyhedral sets is addressed
in this paper. The validation of the positively invariant sets can be
done by solving LPs which can be easily done numerically. It is
illustrated by examples that our checking method is effective. Compared
with the now existing algebraic methods, numerical checking method is an
attractive method in that it’s easy to be implemented.
In Copernicus' day, canons were buried under the altar where they served Mass. As such, the altar of St. Andrew in Frombork cathedral was a natural starting point for researchers looking for the great astronomer's grave.
A research project underway at the Institute of Psychology at the Adam Mickiewicz University in Poznań aims to adapt tools to study the development of young Polish children.
Geological information of the right type and in the right place can help boost public awareness of and appreciation for the geological diversity around us.
Identifying the best scientists among the mediocre is straightforward when given the perspective of centuries, or at least decades, of hindsight. The problem of evaluating contemporary researchers is far more complex.