Open- and closed-loop aberration correction by use of a quadrature interferometric wave-front sensor

Experimental results are presented for an adaptive optics system based on a quadrature Twyman-Green interferometric wave-front sensor. The system uses a circularly polarized reference beam to form two interferograms with a pi/2 phase shift. The experiments conducted used Kolmogorov phase screens to simulate atmospheric phase distortions. Strehl ratio improvements by a factor of 8, to an absolute value of 0.45, are demonstrated.     

Electron density characterization by use of a broadband x-ray-compatible wave-front sensor

The use of a Hartmann wave-front sensor to accurately measure the line-integrated electron density gradients formed in laser-produced and z-pinch plasma experiments is examined. This wave-front sensor may be used with a soft-x-ray laser as well as with incoherent line emission at multikilovolt x-ray energies. This diagnostic is significantly easier to use than interferometery and moiré deflectometry, both of which have been demonstrated with soft-x-ray lasers. This scheme is experimentally demonstrated in the visible region by use of a Shack-Hartmann wave-front sensor and a liquid-crystal spatial light modulator to simulate a phase profile that could occur when an x-ray probe passes through a plasma. The merits of using a Hartmann sensor include a wide dynamic range, broadband or low-coherence-length light capability, high x-ray efficiency, two-dimensional gradient determination, multiplexing capability, and experimental simplicity. Hartmann sensors could also be utilized for wavelength testing of extreme-ultraviolet lithography components and x-ray phase imaging of biological specimens.     

Blow-up examples for second order elliptic PDEs of critical Sobolev growth

Let be a smooth compact Riemannian manifold of dimension , and be the Laplace-Beltrami operator. Let also be the critical Sobolev exponent for the embedding of the Sobolev space into Lebesgue's spaces, and be a smooth function on . Elliptic equations of critical Sobolev growth such as

have been the target of investigation for decades. A very nice -theory for the asymptotic behaviour of solutions of such equations has been available since the 1980's. The -theory was recently developed by Druet-Hebey-Robert. Such a theory provides sharp pointwise estimates for the asymptotic behaviour of solutions of . It was used as a key point by Druet to prove compactness results for equations such as . An important issue in the field of blow-up analysis, in particular with respect to previous work by Druet and Druet-Hebey-Robert, is to get explicit nontrivial examples of blowing-up sequences of solutions of . We present such examples in this article.

     

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R² and their distance functions. The L² norm of the difference of characteristic functions, the L and the W^1,2 norms of the difference of distance functions define interesting topologies, in particular the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ² of positive reach in the sense of Federer [16], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem.We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational definitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples.     

Boc-protected amines via a mild and efficient one-pot Curtius rearrangement

[reaction: see text] The reaction of a carboxylic acid with di-tert-butyl dicarbonate and sodium azide allowed the formation of an acyl azide intermediate, which undergoes a Curtius rearrangement in the presence of tetrabutylammonium bromide and zinc(II) triflate. The trapping of the isocyanate derivative in the reaction mixture led to the desired tert-butyl carbamate in high yields at low temperature. These reaction conditions are compatible with a variety of substrates, including malonate derivatives, which provide access to protected amino acids.     

Redox-active pH-responsive molecules: ferrocenylphosphonic acid, ferrocenylmethylphosphonic acid and 1,1'-ferrocenylbisphosphonic acid. Structural determination of FcPO3Na2.5H2O

The acidity constants of the reduced and oxidized species of ferrocenylphosphonic acids FcPO3H2, FcCH2PO3H2 and fc(PO3H2)2 (Fc = (eta5-C5H5)Fe(eta5-C5H4), fc = (eta5-C5H4)Fe(eta5-C5H4)) in water have been evaluated by potentiometric, 31P NMR, and electrochemical methods. The oxidized forms are more acidic than the reduced ones. The interaction between the redox centre and the charged oxygen atoms of the phosphonate group is shown to be electrostatic. The maximum oxidation shift DeltaE between the protonated and unprotonated species increases with the number of charges of the substrate and decreases with the increase of the distance between the ferrocenyl centre and the oxygen atoms of the phosphonate group. The structure of FcPO3Na2.5H2O is determined. The compound crystallizes in the monoclinic system. It is lamellar with an inorganic layer formed by tetramers Na4O14, the ferrocenyl groups occupying the interlamellar space.     

SHADOC: a multi‐agent model to tackle viability of irrigated systems

The viability of irrigated systems in the Senegal River Valley is being brought into question today due to their underutilization. We assume that their viability depends largely on the way their different components behave and interact. We therefore sought to examine in greater depth today's knowledge of the structure of these systems and activities performed within them. This led to the development of a multiagent system model, a kind of virtual irrigated system, with a special focus on rules in use for access to credit, water allocation and cropping season assessment as well as organization and coordination of farmers. The purpose of this paper is to show how this kind of tool is relevant to the study of irrigated systems' viability. As an example it is used to examine the influence of existing social networks on the viability of irrigated systems.     

Selective alkylation of a 6,7-dihydroxyquinazoline

A convenient 3-step multi-parallel process for the preparation of 4-(3-chloro-2-fluoroanilino)-6,7-bisalkoxyquinazolines is highlighted.     

Electronic structure of Al2O3 from electron energy loss spectroscopy

The electronic structure of Al₂O₃ has been studied by electron energy loss spectroscopy (ELS), and an energy level model of both filled and empty states has been constructed from the ELS and available optical data. For the high temperature pyrolytic α-polycrystalline Al₂O₃ films, the transitions are assumed to originate at the two principal peaks in the valence band density of states and the O(2s) core state, and to terminate on two peaks within the conduction band density of states. We also report energy loss spectra due to excitations out of the deeper Al(2p), Al(2s), Al(1s), and O(1s) core levels. The excitations originating at the Al(2p), Al(2s), and Al(1s) core levels terminate on levels in the conduction band and on an exciton lying about 1 eV below the conduction-band edge.     

Raman bandshape analysis in liquid fluorine

A bandshape study of the Raman diffusion by liquid fluorine over the temperature range 75–100°K is presented. A discussion of the molecular reorientation process is developed.