A Note on the analytic solutions of the Camassa–Holm equation

In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to $H^s(\mathbb{R})$ with $s>3/2$, $6u_0{6}_{L^1}<\infty$ and $u_0?u_{0xx}$ does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Dielectric properties of high-kappa oxides: theory and experiment for Lu2O3

We present a combined experimental and theoretical analysis of the dielectric and vibrational properties of crystalline lutetium oxide in its ground-state bixbyite structure. The vibrational dielectric function of Lu2O3 thin films grown by atomic-layer deposition was studied by infrared transmission and reflection-absorption spectroscopies, selectively accessing transverse and longitudinal optical frequencies. The static dielectric constant is extracted analyzing the infrared response. We also present first-principles density-functional linear-response calculations, which are in close agreement with experiment, and provide insight into the microscopic nature of vibrational spectra and dielectric properties.     

Thiazolidin-4-one formation. Mechanistic and synthetic aspects of the reaction of imines and mercaptoacetic acid under microwave and conventional heating

Microwave irradiation of a mixture of benzylidene-anilines and mercaptoacetic acid in benzene gives 1,3-thiazolidin-4-ones in very high yield (65-90%), whereas the same reaction performed through using the conventional method, at reflux temperature, requires a much longer time and gives a much lower yield (25-69%). This difference seems to be due to some intermediates and by-products formed during the conventional reaction. On the basis of 1H NMR studies, two different mechanisms, acting in benzene and in DMF, respectively, have been hypothesized for the thiazolidin-4-one system formation.     

Monolithic columns with a gradient of functionalities prepared via photoinitiated grafting for separations using capillary electrochromatography

Stationary phases for capillary electrochromatography with a longitudinal gradient of functionalities have been prepared via photoinitiated grafting of polymer chains onto the pore surface of a porous polymer monolith. In order to achieve the desired retention and electroosmotic flow, the hydrophobic poly(butyl methacrylate-co-ethylene dimethacrylate) monolith with optimized porous properties was grafted with a layer of ionizable polymer, poly(2-acrylamido-2-methyl-1-propanesulfonic acid). A moving shutter and a neutral density filter were used to control the dose of UV light received at different locations along the monolith in order to create the longitudinal gradient of functionalities. Formation of the desired gradients was confirmed using electron probe microanalysis of different locations along the column. The preparation technique significantly affects performance in the CEC mode as demonstrated on the separations of a model mixture using columns both with homogeneous distribution of grafts and with a gradient of functionality. Columns grafted with the gradient of functionalities were found superior to those functionalized uniformly. A comparison of the performance of the gradient column with another containing evenly distributed functionalities showed the performance benefits of the "gradient" column.     

MRI characterization of residual mediastinal masses in Hodgkin's disease: long-term follow-up

Our purpose was to evaluate the role of MRI in distinguishing fibrous from active residual masses in treated Hodgkin's disease. Forty patients with residual mediastinal mass larger than 1.5 cm underwent MRI 1, 3, 6, and 12 months after the end of cycles of prescribed chemotherapy or combined chemoradiotherapy. The MRI examinations were performed on a 0.5 and a 1.5 T systems, using T(1) before and after gadolinium injection and T(2)-weighted sequences. Each time the residual mass was evaluated in size and signal intensity on spin echo (SE) T(2)-weighted images and on SE T(1)-weighted images after contrast medium. Low signal intensity and low contrast enhancement were considered signs of inactive residues; homogeneous high signal intensity and high contrast enhancement were indicative of active residual disease; heterogeneous signal intensity and heterogeneous contrast enhancement were indicative of partial remission or necrotic/inflammatory phenomena. MR showed high diagnostic accuracy in the evaluation of Hodgkin's mediastinal residues after treatment, if performed at least 6 months after the end of therapy, reaching the highest sensitivity and specificity values at 12 month follow-up (considering the three parameters-T(2) signal intensity, contrast-enhancement, and size-all together). If we consider the single parameters individually, we can observe that size variation remains the more valuable parameter to predict or to exclude a relapse. MR diagnostic accuracy at the 6-month follow-up was lower due to the higher incidence of inhomogeneous pattern. The accuracy of MR performed at 1 and at 3 months after the end of therapy was not satisfying. This represents a clinical problem because the most important clinical decisions have to be taken just in this early post-treatment phase.     

Complete structural and magnetic characterization of biological radicals in solution by an integrated quantum mechanical approach: glycyl radical as a case study

An integrated quantum mechanical approach for the structural and magnetic characterization of flexible free radicals in solution has been applied to a model of the glycyl radical engaged in peptidic chains. The hyperfine couplings computed using hybrid density functionals and purposely tailored basis sets are in good agreement with experiment when vibrational averaging effects from low frequency motions and solvent effects (both direct H bonding and bulk) are taken into the proper account. The g tensor shows a smaller dependence on the specific form of the density functional, the extension of the basis set over a standard double-zeta+polarization level, vibrational averaging, and bulk solvent effects. However, hydrogen bridges with solvent molecules belonging to the first solvation shell play a significant role. Together with their intrinsic interest, our results show that a comprehensive and reliable computational approach is becoming available for the complete characterization of open-shell systems of biological interest in their natural environment.     

Nearest-neighbor configuration in (GaIn)(NAs) probed by x-ray absorption spectroscopy

Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission.     

Catalytic activity of a ceria-lanthana system for 4-methylpentan-2-ol dehydration

A ceria-lanthana catalytic system prepared by the sol-gel technique proved to be active in 4-methylpentan-2-ol conversion, mainly leading to 4-methylpent-1-ene, a monomer for manufacturing polymers of high technological properties. The product distribution strongly depends on the acid-base features of the catalyst. The catalytic behavior of the samples was examined in the light of their acid-base properties. This revised version was published online in June 2006 with corrections to the Cover Date.     

"Oscillating" metallocene catalysts: what stops the oscillation?

The 150 MHz (13)C NMR microstructural analysis of polypropylene samples produced with two representative "oscillating" metallocene catalysts of largely different steric hindrance, namely [(2-(3,5-di-tert-butyl-4-methoxyphenyl)indenyl)(2)ZrP](+) and [(2-phenylindenyl)(2)ZrP](+) (P = polymeryl), and the implications on the origin of the stereocontrol are presented and discussed in detail. The original mechanistic proposal of an "oscillation" between a rac-like (isotactic-selective) and a meso-like (nonstereoselective) conformation cannot explain the observed polymer configuration. The isotactic-stereoblock nature of the polymers obtained with the former catalyst proves unambiguously that the active cation "oscillates" between the two enantiomorphous rac-like conformations at an average frequency that, even at high propene concentration, is only slightly lower than that of monomer insertion. The less-hindered [(2-phenylindenyl)(2)ZrP](+) gives instead a largely stereoirregular polypropylene, which is the logical consequence of a faster ligand rotation; however, depending on the use conditions (in particular, on the nature of the cocatalyst and the polarity of the solvent), the polymerization products may also contain appreciable amounts of a fairly isotactic fraction. The peculiar microstructure of this fraction, with isotactic blocks of the same relative configuration spanned by very short atactic ones, rules out the possibility that the latter are due to an active species in meso-like conformation and points rather to a conformationally "locked" rac-like species with restricted ring mobility. The hypothesis of a stereorigidity induced by the proximity to a counteranion, which would play the role of the interannular bridge in the rac-bis(indenyl) ansa-metallocenes, was tested by computer modeling on a [rac-(2-phenylindenyl)(2)ZrMe(C(3)H(6))][B(C(6)F(5))(4)] ion couple and found viable.