Newton's method on Riemannian manifolds: covariant alpha theory

In this paper, Smale's theory is generalized to the contextof intrinsic Newton iteration on geodesically complete analyticRiemannian and Hermitian manifolds. Results are valid for analyticmappings from a manifold to a linear space of the same dimension,or for analytic vector fields on the manifold. The invariant is defined by means of high-order covariant derivatives. Boundson the size of the basin of quadratic convergence are given.If the ambient manifold has negative sectional curvature, thosebounds depend on the curvature. A criterion of quadratic convergencefor Newton iteration from the information available at a pointis also given.     

Helstrom Bound for Squeezed Coherent States in Binary Communication

In quantum information processing, using a receiver device to differentiate between two non-orthogonal states leads to a quantum error probability. The minimum possible error is known as the Helstrom bound. In this work, we study the conditions for state discrimination using an alphabet of squeezed coherent states and compare them with conditions using the Glauber-Sudarshan, i.e., standard, coherent states.     

Improvements for ground-based remote sensing of atmospheric aerosol properties by additional polarimetric measurements

We discuss the improvements in the aerosol properties characterization resulting from the additional multi-wavelength polarization measurements measured by a new CIMEL polarized sun/sky-photometer, CE318-DP. In order to process direct-sun, sky and polarization measurements in a wide spectral range (340–1640 nm), we developed new calibration methods and strategies, e.g. using the Langley plot method to calibrate both direct-sun irradiance and sky radiance, as well as combining laboratory facilities with a vicarious method to calibrate the polarized sky measurements. For studying the impact of new polarimetric measurements on the retrievals of aerosol properties, we have processed an extensive record of field measurements using an updated Dubovik and King retrieval algorithm [Dubovik O, Sinyuk A, Lapyonok T, Holben BN, Mishchenko MI, et al. Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust. J Geophys Res 2006;111:D11208.]. A preliminary analysis shows that adding polarization in the inversion can reduce possible errors (notably for about 30% of our field cases) in the fine mode size distribution, real part of refractive index and particle shape parameter retrievals, especially for small particles.     

Design of metal oxide nanoparticles: Control of size,shape, crystalline structure and functionalization by aqueous chemistry

The aim of this paper is to show that a very simple but well controlled chemistry in an aqueous medium allows one to efficiently control the main characteristics of oxide nanoparticles. Examples concerning titania, alumina, iron and manganese oxides are discussed to illustrate various effects on the control of size, shape and structure of nanoparticles. Some examples of functionalization of these particles are also illustrated. Experimental data, procedures and detailed references can be found in the cited literature.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Photoinduced formation of a cryptand from a coronand: an unexpected switch in cation binding affinity

Aza-crown ethers 2 and 3 with anthracene-containing pendant arms have been synthesised and characterised. Both compounds bind Group 1 metal cations in solution, forming complexes of 1:1 stoichiometry. The properties of compound 2 and its complexes have been studied by a range of techniques, including NMR, UV and fluorescence spectroscopy and X-ray crystallography. The pendant arms can adopt either a cis or a trans geometry, the cis geometry favoured with larger cations. The geometry of the complex affects the fluorescence properties of the system, with larger cations giving higher excimer/monomer ratios. Upon irradiation at lambda>300 nm, coronand 2 forms the cryptand 5 through a reversible intramolecular [4pi+4pi] cycloaddition reaction. The rates of the forward and reverse reactions of this photochromic process are cation dependent; in particular the rate of the thermal reverse reaction is decreased by smaller cations and increased by larger cations, especially Rb(+). The metal binding constants in methanol for 2 and 5 have been determined, revealing that the cryptand 5 binds Na(+) and Rb(+) more weakly than crown ether 2 by over two orders of magnitude.     

An efficient synthesis of the new benzo[c]pyrido[2,3,4-kl]acridine skeleton

A series of molecules of therapeutic interest, possessing the new skeleton of 1H-benzo[c]pyrido[2,3,4-kl]acridine with acyl or aminoacyl and methoxy or aminoalkoxy substituents on the aromatic homocycles were synthesized by means of a Friedl?nder-type reaction. The requisite 5-aminodihydroquinoline-4-ones 1, whose preparation is described, were reacted with the appropriate alpha-tetralones 2 using an acidic catalyst (PPTS) under azeotropic conditions. Optimized reaction time and yield depend on temperature, which must not be below 90 degrees C.     

Reactions of Metal Salts and Alkali Metal Nitrates. Role of the Metal Precursors and Alkali Metal Ions in the Resulting Phase of Zirconia

Zirconia powders are prepared by reaction of a zirconium precursor with an alkali metal nitrate. The major part of the reactions takes place before the melting points and then the reactions go slowly to completion at 450°C in the molten salts. The roles of the precursor and the alkali metal ion are discussed considering the reaction between two precursors, octahydrated zirconium oxychloride and zirconium tetrachloride, and two nitrates, LiNO₃ and NaNO₃, and some resulting physico-chemical differences. The obtained zirconia powders contain very small amounts of alkali metal ions which act as stabilizing agent. Their effect on the balance tetragonal-monoclinic ZrO₂ depends upon the homogeneity of their distribution which is related to their ability to diffuse inside the bulk of particles and their polarizing power when located mainly on the surface.