In this short note, we study Lehmer’s conjecture in terms of stability theory. We state Bounded conjecture, and prove that if a certain formula is uniformly stable class structures, then holds. Our proof based on Van der Waerden’s theorem from additive combinatorics.

This paper is motivated by a class of positive systems with an input that subject to unknown state-dependent power law delay as well saturation. For example, biological networks have non-negative protein concentration states. Mass action kinetics in these result behavior, while complex interactions cause signal propagation delays. Incomplete network characterization makes state-dependence unkno...

Abstract. We study the convergence of the Kähler-Ricci flow on a Fano manifold under some stability conditions. More precisely we assume that the first eingenvalue of the ∂̄-operator acting on vector fields is uniformly bounded along the flow, and in addition the Mabuchi energy decays at most logarithmically. We then give different situations in which the condition on the Mabuchi energy holds.

This note describes a logic-based hybrid controller for the well-studied nonholonomic integrator. Our controller provides Lyapunov stability and is designed so that the control signals remain uniformly bounded and have at most a nite number of discontinuities in any nite interval. In particular, no \chattering" occurs. Two alternative controllers, which use only partial state information, are a...

Abstract. Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the ...

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.

A systematic way to combine adaptive control and sliding mode control (SMC) for trajectory tracking of robot manipulators in the presence of parametric uncertainties and uncertain nonlinearities is developed. Continuous sliding mode controllers without reaching transients and chattering problems are rst developed by using a dynamic sliding mode. Transient performance is guaranteed and globally ...

In this paper, we study the stability and generalization properties of penalized empirical-risk minimization algorithms. We propose a set of properties of the penalty term that is sufficient to ensure uniform β-stability: we show that if the penalty function satisfies a suitable convexity property, then the induced regularization algorithm is uniformly β-stable. In particular, our results imply...