Search results for " surface"
showing 10 items of 2838 documents
Multidomain spectral method for the Gauss hypergeometric function
2018
International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…
Homeomorphic graph manifolds: A contribution to the μ constant problem
1999
Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.
Dosimetry comparison between TG-43 and Monte Carlo calculations using the Freiburg flap for skin high-dose-rate brachytherapy
2012
Abstract Purpose The purpose of this work was to evaluate whether the delivered dose to the skin surface and at the prescription depth when using a Freiburg flap applicator is in agreement with the one predicted by the treatment planning system (TPS) using the TG-43 dose-calculation formalism. Methods and Materials Monte Carlo (MC) simulations and radiochromic film measurements have been performed to obtain dose distributions with the source located at the center of one of the spheres and between two spheres. Primary and scatter dose contributions were evaluated to understand the role played by the scatter component. A standard treatment plan was generated using MC- and TG-43-based TPS appl…
FT-IR Investigation of the Urea State in AOT Reversed Micelles
2001
Abstract FT-IR spectra of the urea/sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/CCl 4 system as a function of the urea-to-AOT molar ratio ( R urea ) at a fixed AOT concentration ([AOT]=0.1 mol·kg −1 ) have been recorded at 25°C. The experimental data are consistent with the hypothesis that at low R urea values urea is dispersed as monomers among the hydrophilic core of AOT reversed micelles, whereas at R urea >0.13 it is encapsulated as small molecular clusters. These clusters display some departures from the H-bonded structure of the pure solid urea attributable to their small size and to urea–AOT head group interactions. The stretching modes of AOT sulfonate groups are affected by the pr…
Halloysite nanotubes as nanoreactors for heterogeneous micellar catalysis
2021
Abstract Hypothesis Electrostatic attractions between the anionic head group of sodium alkylsulphates and the positively charged inner surface of halloysite nanotubes (HNTs) drive to the formation of tubular inorganic micelles, which might be employed as nanoreactors for the confinement of non polar compounds in aqueous media. On this basis, sodium alkylsulphates/halloysite hybrids could be efficient nanocatalysts for organic reactions occurring in water. Experiments Sodium decylsulphate (NaDeS) and sodium dodecylsulphate (NaDS) were selected for the functionalization of the halloysite cavity. The composition, the structure and the surface charge properties of the hybrid nanotubes were dete…
The crucial interactions between climate and soil
2022
Since the birth of soil science, climate has been recognized as a soil-forming factor, along with parent rock, time, topography, and organisms (from which humans were later kept distinct), often prevalent on the other factors on the very long term. But the climate is in turns affected by soils and their management. This paper describes the interrelationships between climate – and its current change – and soil, focusing on each single factor of its formation. Parent material governs, primarily through the particle size distribution, the capacity of soil to retain water and organic matter, which are two main soil-related drivers of the climate. Time is the only unmanageable soil-forming facto…
A Theoretical Study of the Favorskii Rearrangement. Calculation of Gas-Phase Reaction Paths and Solvation Effects on the Molecular Mechanism for the …
1997
The molecular mechanism of the α-chlorocyclobutanone transposition to yield cyclopropanecarboxylic acid, as a model of the Favorskii rearrangement, has been theoretically characterized in vacuo by means of ab initio molecular orbital procedures at the Hartree−Fock (HF) level of theory with the 6-31G* and 6-31+G* basis sets. The electron correlation has been estimated at the MP2/6-31G* level and calculations based on density functional theory, BLYP/6-31G*. The solvent effects are included at HF/6-31G* level by means of a polarizable continuum model. The questions related to the two accepted molecular mechanisms, the semibenzilic acid and the cyclopropanone transpositions, as well as the comp…
Über die Elementarreaktionen der radikalischen Polymerisation von Benzylmethacrylat
1973
Durch Kombination stationarer und instationarer Methodik (rotierender Sektor) werden die Absolutwerte der Geschwindigkeitskonstanten von Kettenwachstum und Kettenabbruch von Benzylmethacrylat unter dem Einflus verschieden viskoser Losungsmittel bestimmt. Die Radikalausbeute f hangt von der Viskositat des Losungssystems und der Art der Monomeren, dagegen nicht (oder fast nicht) von der Konzentration des Monomeren und der Geschwindigkeit der Radikalerzeugung ab. Daraus wird geschlossen, das ein merklicher Anteil von Zwillingsrekombinationen auserhalb des primaren Losungsmittelkafigs stattfindet. Die Geschwindigkeitskonstante kw des Kettenwachstums stimmt praktisch uberein mit der des Methylme…
Heterometallic Titanium–Organic Frameworks by Metal-Induced Dynamic Topological Transformations
2020
Reticular chemistry has boosted the design of thousands of metal and covalent organic frameworks for unlimited chemical compositions, structures, and sizable porosities. The ability to generate porous materials at will on the basis of geometrical design concepts is responsible for the rapid growth of the field and the increasing number of applications derived. Despite their promising features, the synthesis of targeted homo- and heterometallic titanium–organic frameworks amenable to these principles is relentlessly limited by the high reactivity of this metal in solution that impedes the controlled assembly of titanium molecular clusters. We describe an unprecedented methodology for the syn…
Comments on surface structure analysis by water and nitrogen adsorption
2004
Specific surface area and pore size distribution are determined usually from adsorption isotherms at low temperatures using nitrogen or noble gases. These are not absolute parameters and the measuring methods are fraught with serious difficulties. General problems of sorption measurements and recent developments are discussed. To obtain information for practical purposes these measurements need to be supplemented by investigations of the sorbate/sorbent system used in practice. Results of the measurement of nitrogen and water vapour adsorption on different materials are compared.