Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Human-Robot Dichotomy

This paper belongs to the area of roboethics and responsible robotics. It discusses the conceptual and practical separation of humans and robots in designing and implementing robots into real-world environments. We argue here that humans are often seen as a component that is only optional in design thinking, and in some cases even an obstacle to the successful robot performance. Such an approach may vary from viewing humans as a factor that does not belong to the robotics domain, through attempts to ‘adjust’ humans to robot requirements, to the overall replacement of humans with robots. Such separation or exclusion of humans poses serious ethical challenges, including the very exclusion of ethics from our thinking about robots

Negation and Dichotomy

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition

The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor