Brockett's necessary condition yields a test to determine whether system can be made stabilize about some operating point via continuous, purely state-dependent feedback. For many real-world systems, however, one wants sets which are more general than single point. One also control such systems operate safely by making obstacles and other "dangerous" repelling. styl...

Abstract Let $$\Omega $$ Ω be a smooth, bounded, convex domain in $${\mathbb {R}}^n$$ R n and let $$\Lambda _k$$ Λ k finite subset of . We find necessary geometric condition...

The bilevel program is an optimization problem in which the constraint involves solutions to a parametric problem. It well known that value function reformulation provides equivalent single-level problem, but it results nonsmooth never satisfies usual qualification, such as Mangasarian–Fromovitz qualification (MFCQ). In this paper, we show even first order sufficient condition for metric subreg...

We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative potentials, criterion is an if and only condition. The formulated sign-flipped Kirkwood-Salsburg operator known conditions such as Koteck${\'y}$-Preiss Fern${\'a}$ndez-Procacci are easily recovered. In addition, we...