In this note, we show how to marginalize over the damping parameter of the PageRank equation so as to obtain a parameter-free version known as TotalRank. Our discussion is meant as a reference and intended to provide a guided tour towards an interesting result that has applications in information retrieval and classification.

In this article we consider an n-dimentional thermoelastic system with a viscoelastic damping localized on a part of the boundary. We establish an explicit and general decay rate result that allows a larger class of relaxation functions and generalizes previous results existing in the literature.

In this paper we present the first extension of the backstepping methods developed for control of parabolic PDEs (modeling thermal, fluid, and chemical reaction dynamics, including Navier-Stokes equations and turbulence) to secondorder PDE systems (often referred loosely as hyperbolic) which model flexible structures and acoustic. We introduce controller and observer designs capable of adding d...

We study a stabilization problem of system coupled by wave and Euler–Bernoulli plate equation. Only one the two equations is directly damped. Under some assumptions on damping coupling terms, we prove that sufficiently smooth solutions decay logarithmically without any geometric conditions domain. The proofs these results rely interpolation inequalities for elliptic-parabolic estimate resolvent...