Uncertainty estimation in chemical measurements: carbon dioxide determination at atmospheric concentration

The present work deals with the evaluation of measurement uncertainty in the determination of carbon dioxide (CO2) concentration in atmosphere, given the high relevance of this greenhouse gas that influences earth climate. In order to carry out CO2 measurements, non dispersive infrared (NDIR) analysers are usually employed as they are stable and scarcely affected by interferences from other air components or pollutants. Typical uncertainty sources are the resolution of the analyser, its time drift and the contributions due to instrument calibration, which is required in order to produce traceable measurement results. The calibration uncertainty takes into account the uncertainty of the composition of the calibration gas mixtures, the instrument repeatability and the possible or residual lack of fit of the adopted mathematical model.     

Conservation of Resonant Periodic Solutions for the One-Dimensional Nonlinear Schrödinger Equation

We consider the one-dimensional nonlinear Schrödinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the mass term). We investigate conservation of small amplitude periodic solutions for a large measure set of frequencies. In particular we show that there are infinitely many periodic solutions which continue the linear ones involving an arbitrary number of resonant modes, provided the corresponding frequencies are large enough, say greater than a certain threshold value depending on the number of resonant modes. If the frequencies of the latter are close enough to such a threshold, then they can not be too distant from each other. Hence we can interpret such solutions as perturbations of wave packets with large wave number.     

Padé–type rational and barycentric interpolation

In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin. Thus, the interpolants constructed in this way possess a Padé–type property at 0. Numerical examples show the interest of the procedure. The interpolation procedure can be easily modified to introduce a partial knowledge on the poles and the zeros of the function to approximated. A strategy for removing the spurious poles is explained. A formula for the error is proved in the real case. Applications are given.     

Borcea–Voisin Calabi–Yau threefolds and invertible potentials

We prove that the Borcea–Voisin mirror pairs of Calabi–Yau threefolds admit projective birational models that satisfy the Berglund–Hübsch–Chiodo–Ruan transposition rule. This shows that the two mirror constructions provide the same mirror pairs, as soon as both can be defined.     

Sharp geometric condition for null-controllability of the heat equation on $$\mathbb {R}^d$$ and consistent estimates on the control cost

In this note we study the control problem for the heat equation on \(\mathbb {R}^d\), \(d\ge 1\), with control set \(\omega \subset \mathbb {R}^d\). We provide a necessary and sufficient condition (called \((\gamma , a)\)-thickness) on \(\omega \) such that the heat equation is null-controllable in any positive time. We give an estimate of the control cost with explicit dependency on the characteristic geometric parameters of the control set. Finally, we derive a control cost estimate for the heat equation on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the control sets are again assumed to be thick. We show that the control cost estimate is consistent with the \(\mathbb {R}^d\) case.     

Integrating Operations Research in Constraint Programming

This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.