Abstract: In this paper, we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input-output and state properties. Specifically, a stochastic version of dissipativity ...

ABSTRACT: We prove that the Collatz, 3n+1 , conjecture is true. To prove this statement, we will first see that, if a number n starts a sequence that satisfies the Collatz conjecture then all ...

For centuries, astronomers have sought to understand the formation and evolution of the solar system and the dynamics that ...

More specifically, Lyapunov exponents and their variants may not work well for nonlinear regimes, while information-theory-based methods may not be directly applicable to high-dimensional dynamical ...

The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville–Arnold and Mischenko–Fomenko integrability. This sets the stage for such ...

This is what may happen if organizations invest heavily in digital security but overlook the most common point of failure: ...

Designer Sebastiaan de With has published an impressive preview of what Apple's rumored iOS redesign might look like, ...

Astronomers have just discovered a new celestial body in our solar system that could challenge major space theory. 2017 OF201 ...

Terrain Theory is a medical theory that emphasizes the importance of the internal environment of the body, or "terrain," as a critical factor in determining health. In Terrain Theory, germs are not ...

Deadlier weapons, more nations, autocrats in charge, disinformation and collapsing arms control — the risk of nuclear ...