This paper relates properties of operators with the well-known concepts of positive realness and passivity properties in dynamic systems and their associate transfer functions. Those concepts together with very close related ones are first examined from a physical point of view. Then, they are related with hyperstability and properties of transfer functions while the hyperstability theorem is r...

A component of the equilibria of a finite game is hyperstable if and only if its index is nonzero.

This short paper presents an hyperstability theorem for hybrid dynamic systems composed of coupled differential and difference equations subject to time varying nonlinearities satisfying a Popov ' s type inequality . Some corollaries and related physical interpretations are also given.

According to a prevailing theory, (2S,4R)-4-hydroxyproline (Hyp) residues stabilize the collagen triple helix via a stereoelectronic effect that preorganizes appropriate backbone torsion angles for triple-helix formation. This theory is consistent with the marked stability that results from replacing the hydroxyl group with the more electron-withdrawing fluoro group, as in (2S,4R)-4-fluoroproli...

We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.