We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or F -Sobolev). The case of Poincaré and weak Poincaré inequalities was studied in [2]. This approach allows us to recover and extend in an unified way some known criteria in the euclidean case (BakryEmery, Wang, Kusuoka-Stroock ...).

The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper to compute. This allows performing a lowcost screening of unessential variabl...

The authors analyze dynamical properties of daily surface pressure, surface temperature and precipitation rate using two parameters from a universal distribution derived in previous research from extreme value theory of Poincaré recurrences. The two parameters, local dimension of the phase space attractor and the inverse of the average residence time, are physically intuitive, and have the pote...

The authors analyze dynamical properties of daily surface pressure, surface temperature and precipitation rate using two parameters from a universal distribution derived in previous research from extreme value theory of Poincaré recurrences. The two parameters, local dimension of the phase space attractor and the inverse of the average residence time, are physically intuitive, and have the pote...

Natural languages are ill-suited to express mathematical reasoning. The purpose of an artificial language-predicate logic-with a deduction system is to enable us to express reasoning clearly and concisely. In this article we give two examples illustrating how Gentzen's system of 'natural de-duction' [2] fails to meet the case. In [1], the following problem is stated and solved: Given two casket...

We study the lower and upper local rates of Poincaré recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincaré recurrence of an ergodic dynamical system (X,F, μ, T ) is greater or equal to 1 μ-almost everywhere, then it is weakly mixing.

BACKGROUND Heart rate variability (HRV) is known to be impaired in patients with congestive heart failure (CHF). Time-domain analysis of ECG signals traditionally relies heavily on linear indices of an essentially non-linear phenomenon. Poincaré plots are commonly used to study non-linear behavior of physiologic signals. Lagged Poincaré plots incorporate autocovariance information and analysis ...

This paper presents a simple nonautonomous circuit with a periodic pulse-train input. If the input does not exist, the circuit exhibits either equilibrium attractor or hard oscillation. If a periodic pulse-train input is applied, the circuit exhibits interesting chaotic and periodic attractors. The circuit behavior can be analyzed by a mapping procedure based on a 1-D return map focusing on the...

for every rational function ƒ with poles off K. In this note it is shown that any operator for which the spectrum is a spectral set has a nontrivial invariant subspace. In [6] von Neumann introduced the notion of spectral set and showed that if T has II T\\ = 1 then the closed unit disc, D"~, is a spectral set for T. For this reason any operator whose spectrum is a spectral set is called a von ...

This paper considers synchronous phenomena from switchcoupled relaxation oscillators. This system exhibits a variety of interesting superstable synchronous phenomena. Using a hybrid return map, we can analyze the phenomena almost completely. Using a simple circuit, typical phenomena are verified in the laboratory.