On the Almost Everywhere Continuity

The aim of this paper is to provide characterizations of the Lebesgue-almost everywhere continuity of a function f : [a, b] $\rightarrow$ R. These characterizations permit to obtain necessary and sufficient conditions for the Riemann integrability of f

On the multiplier rules

We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. In comparison with existing results we weaken assumptions of continuity and of differentiability.Comment: 9 page

Discrete time pontryagin principles in banach spaces

The aim of this paper is to establish Pontryagin's principles in a dicrete-time infinite-horizon setting when the state variables and the control variables belong to infinite dimensional Banach spaces. In comparison with previous results on this question, we delete conditions of finiteness of codi-mension of subspaces. To realize this aim, the main idea is the introduction of new recursive assumptions and useful consequences of the Baire category theorem and of the Banach isomorphism theorem

Infinite Dimensional Multipliers and Pontryagin Principles for Discrete-Time Problems

The aim of this paper is to provide improvments to Pontryagin principles in infinite-horizon discrete-time framework when the space of states and of space of controls are infinite-dimensional. We use the method of reduction to finite horizon and several functional-analytic lemmas to realize our aim

Pontryagin principle for a Mayer problem governed by a delay functional differential equation

We establish Pontryagin principles for a Mayer's optimal control problem governed by a functional differential equation. The control functions are piecewise continuous and the state functions are piecewise continuously differentiable. To do that, we follow the method created by Philippe Michel for systems governed by ordinary differential equations, and we use properties of the resolvent of a linear functional differential equation

Euler-lagrange equation for a delay variational problem

We establish Euler-Lagrange equations for a problem of Calculus of variations where the unknown variable contains a term of delay on a segment

What is new in the prevention of ventilator-associated pneumonia?

Purpose of review: Ventilator-associated pneumonia (VAP) remains a frequent and severe complication in endotracheally intubated patients. Strict adherence to preventive measures reduces the risk of VAP. The objective of this paper is to review what has come forward in recent years in the nonpharmacological prevention of VAP. Recent findings: It seems advantageous to implement care bundles rather than single prevention measures. A solid basis of knowledge seems necessary to facilitate implementation and maintain a high adherence level. Continuous educational efforts have a beneficial effect on attitude toward VAP. Intermittent subglottic secretions drainage, continuous lateral rotation therapy, and polyurethane cuffed endotracheal tubes decrease the risk of pneumonia. In an in-vitro setting, an endotracheal tube with a taper-shaped cuff appears to better prevent fluid leakage compared to cylindrical polyurethane or polyvinylchloride cuffed tubes. Cuff pressure control by means of an automatic device and multimodality chest physiotherapy need further investigation, as do some aspects of oral hygiene. Summary: New devices and strategies have been developed to prevent VAP. Some of these are promising but need further study. In addition, more attention is being given to factors that might facilitate the implementation process and the challenge of achieving high adherence rates