Fast regularized linear sampling for inverse scattering problems

A new numerical procedure is proposed for the reconstruction of the shape and volume of unknown objects from measurements of their radiation in the far field. This procedure is a variant and the linear sampling method has a very acceptable computational load and is fully automated. It is based on exploiting an iteratively computed truncated singular‐value decomposition and heuristics to extract the desired signal from the background noise. Its performance on a battery of examples of different types is shown to be promising. Copyright © 2010 John Wiley & Sons, Ltd.     

Asymptotic analysis of the steady stokes equation with randomly perturbed viscosity in a thin tube structure

The Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε ≪ 1 and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved. Bibliography: 11 titles. Illustrations: 3 figures.     

Sol-gel preparation and properties of interpenetrating, encapsulating and blend silica-based urea-formaldehyde hybrid composite materials

Four different silica-based urea-formaldehyde (UF/SiO₂) composite materials were prepared by various sol-gel synthetic procedures to yield an interpenetrating (IPN-UF/SiO₂), a micro-size UF resin encapsulated inside silica shell (Encap-UF/SiO₂), a micro-size silica encapsulated inside UF shell (Encap-SiO₂/UF), and a blend mixture (Blend-UF/SiO₂) hybrid systems. The thermal properties of the obtained organic-inorganic hybrid composite materials were examined by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The structure and morphology of the obtained systems were investigated by infrared spectroscopy (FT-IR), powder X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. Their surface porosity and acidity were evaluated from the nitrogen adsorption isotherm and the pH of the corresponding 10% aqueous suspension, respectively. All the results provided evidence for the formation of different hybrid systems with different surface, structural and morphological characteristics.     

Optimized FIB silicon samples suitable for lattice parameters measurements by convergent beam electron diffraction

The aim of this paper is to check the effect of artefacts introduced by focused ion beam (FIB) milling on the strain measurement by convergent beam electron diffraction (CBED). We show that on optimized silicon FIB samples, the strain measurement can be performed with a sensitivity of about 2.5 × 10⁻⁴ which is very close to the theoretical one and we conclude that FIB preparation can be suitable for such measurements in microelectronic devices.

To achieve this, we first used CBED and electron energy loss spectroscopy (EELS) which provide a procedure permitting an exact knowledge of the sample geometry, i.e. the thickness of both amorphous and crystalline layers. This procedure was used in order to measure the FIB-amorphized sidewall layer. It was found that if the FIB preparation is optimized one can reduce this amorphous layer down to around 7 nm on each side. Secondly different preparation techniques (cleavage, Tripod™ and FIB) permit to check if the surface damaged layer introduced by FIB influences the strain state of the sample. Finally, it was found that the damaged layer does not introduce measurable strain in pure silicon but reduces appreciably the quality of the CBED patterns.     

Organocatalytic Enantioselective Synthesis of Pyrazoles Bearing a Quaternary Stereocenter

An efficient one‐pot asymmetric synthesis of pyrazoles bearing a chiral quaternary stereocenter has been developed. Quinine‐derived thiourea catalyzed the enantioselective addition of pyrazolones to isatin‐derived ketimines, providing the corresponding acetylated pyrazoles after in situ treatment with Ac₂O/Et₃N. The corresponding pyrazoles were afforded in high yields and excellent enantioselectivities.     

Three‐dimensional framework structures: isomorphous bis(2,6‐diamino‐3,5‐dibromopyridinium) tetrabromidometallate(II) salts with CdII and MnII

In the structural motifs of two isomorphous triclinic salts, (C₅H₆Br₂N₃)₂[MBr₄] (M = Cd^II and Mn^II), each [MBr₄]²⁻ anion interacts with eight surrounding 2,6‐diamino‐3,5‐dibromopyridinium cations through intermolecular C/N—H...Br and Br...Br interactions, leading to a three‐dimensional framework structure. The cations show a minor degree of π–π stacking, adding extra stability to the three‐dimensional architecture.     

Three isomorphous 2,6‐dibromopyridinium tetrabromidometallates: (C5H4Br2N)2[MBr4]·2H2O (M = Cu,Cd and Hg)

The structures of three isomorphous compounds, namely bis(2,6‐dibromopyridinium) tetrabromidocuprate(II) dihydrate, (C₅H₄Br₂N)₂[CuBr₄]·2H₂O, bis(2,6‐dibromopyridinium) tetrabromidocadmate(II) dihydrate, (C₅H₄Br₂N)₂[CdBr₄]·2H₂O, and bis(2,6‐dibromopyridinium) tetrabromidomercurate(II) dihydrate, (C₅H₄Br₂N)₂[HgBr₄]·2H₂O, show a crystal supramolecularity represented by M—Br...H—O—H...Br—M intermolecular interactions along with (π)N—H...OH₂ hydrogen‐bonding interactions forming layers connected via aryl–aryl face‐to‐face stacking of cations, leading to a three‐dimensional network. The anions have significantly distorted tetrahedral geometry and crystallographic C₂ symmetry. The stability of this crystal lattice is evidenced by the crystallization of a whole series of isomorphous compounds.