Laboratory spectroscopic calibration of infrared tunable laser spectrometers for the in situ sensing of the Earth and Martian atmospheres

This paper reports the laboratory spectroscopic calibration of near- and mid- infrared tunable laser spectrometers used to determine in situ trace gases in the middle atmosphere of the Earth or in development for the investigation of the Martian atmosphere. The use of infrared absorption spectroscopy to measure gas concentrations requires a proper knowledge of the rotation–vibration spectra of the targeted molecules as well as a proper investigation of the tunable laser spectral emission properties. This last point is of particular importance for the use of new-generation lasers like quantum-cascade lasers or room-temperature multi-quantum wells laser diodes emitting between 2 and 3 μm. Purposely, we have developed various laboratory tunable laser set-ups to obtain accurate line strengths and pressure-broadening coefficients of atmospheric molecules and to test the performances of cutting-edge laser technology for trace gas sensing. In this paper, the spectroscopic calibration work is described. Several atmospheric applications of tunable laser are reported to stress the impact on concentration retrieval of a proper spectroscopic calibration work. PACS 07.57.T; 93.85; 07.87     

Correlations whose squares are perspectivities

This article concerns itself with correlations of finite projective planes which enjoy the property that their squares are non-trivial perspectivities of the plane. Existence results are obtained and actual constructions are carried out, along the lines established in the study of polarities.It is shown that planes of non-square order do not admit correlations whose squares are elations. Also, that planes of odd non-square order do not admit correlations whose squares are homologies of odd order, while planes of even non-square order do not admit any correlations whose squares are homologies.In Desarguesian planes, the connection between the correlations that we are interested in and unitary polarities is made apparent. In the process, the first infinite family of correlations with exactly one absolute point is obtained.Finally, in a non-Desarguesian plane, an example is displayed of a correlation whose square is an elation.This research was supported in part by New York Institute of Technology.     

An approximation theorem for sections of reflexive sheaves

 We show that, if X is a Stein manifold and D ? X an open set (not necessarily Stein) such that the restriction map has dense image, then, for any reflexive coherent analytic sheaf ℱ on X, the map has dense image, too. We also characterize the reflexivity of a torsion-free coherent sheaf on complex manifolds in terms of absolute gap sheaves or Kontinuit?tssatz. Received: 14 September 2001 / Revised version: 29 January 2002     

Possible transition from rod-like to disc-like behaviour in ortho-metallated imine complexes of palladium(II): crystal and molecular structure of three palladium complexes

Two series of ortho-metallated palladium imine complexes are reported that contain a coordinated β-diketonate group. In one group the chain length of the imine is varied while the β-diketone is unchanged; in the other the imine chains are both fixed as methoxy and the structure of the β-diketonate is varied. The mesomorphism of these new complexes is reported and discussed in relation to the search for materials showing a biaxial nematic phase.     

Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities

In 1956, R. Penrose studied best-approximate solutions of the matrix equation AX = B. He proved that A⁺B (where A⁺ is the Moore-Penrose inverse) is the unique matrix of minimal Frobenius norm among all matrices which minimize the Frobenius norm of AX ? B. In particular, A⁺ is the unique best-approximate solution of AX = I. The vector version of Penrose's result (that is, the fact that the vector A⁺b is the best-approximate solution in the Euclidean norm of the vector equation Ax = b) has long been generalized to infinite dimensional Hilbert spaces.In this paper, an infinite dimensional version of Penrose's full result is given. We show that a straightforward generalization is not possible and provide new extremal characterizations (in terms of the Hermitian order) of A⁺ and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least-squares solutions. For a certain class of operators, we can phrase our characterizations in terms of a whole class of norms (including the Hilbert-Schmidt and the trace norms), thus providing new extremal characterizations even in the matrix case. We treat both operators with closed range and with not necessarily closed range. Finally, we characterize A⁺ as the unique inner inverse of minimal Hilbert-Schmidt norm if ∥A⁺∥₂ < ∞. We give an application of the new extremal characterization to the compensation problem in systems analysis in infinite-dimensional Hilbert spaces.     

A note on the stabilizability of stochastic heat equations with multiplicative noiseSur la stabilisabilité des équations de la chaleur stochastiques avec bruit multiplicatif

We show that a stochastic heat equation with multiplicative noise on a bounded domain $\text{D}$ can be stabilized by a control acting only on a subdomain $\text{O}\text{?}\text{D}$ if $\text{D}\text{?}\text{O}$ is sufficiently ‘thin’. We consider both linear and semilinear stochastic heat equations. To cite this article: V. Barbu et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 311–316.