Three multicomponent reactions of 3,5-dimethyl-4-nitroisoxazole

The title compound is used to prepare 3-arylglutaric acids, bis-isoxazoles and bis-pyrazoles from commercially available materials. The methodologies described have afforded important synthetic intermediates in high yields and without the use of chromatography.     

Weights,growth, and amenability

This paper is a collection of general results in geometric group theory, concerning, in particular, amenability and its relation with growth of groups, cohomology and weights. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional Analysis, 2007.     

Evolution Equations on Non-Flat Waveguides

We investigate the dispersive properties of evolution equations on waveguides with a non-flat shape. More precisely, we consider an operator $$H=-\Delta_{x}-\Delta_{y}+V(x,y)$$ with Dirichlet boundary conditions on an unbounded domain ??, and we introduce the notion of a repulsive waveguide along the direction of the first group of variables, x. If ?? is a repulsive waveguide, we prove a sharp estimate for the Helmholtz equation Hu???u?=?f. As consequences, we prove smoothing estimates for the Schr?dinger and wave equations associated to H, and Strichartz estimates for the Schr?dinger equation. Additionally, we deduce that the operator H does not admit eigenvalues.     

Influence of zirconium on the structure of pristine and leached soda-lime borosilicate glasses: Towards a quantitative approach by O MQMAS NMR

¹⁷O MQMAS NMR was used to characterize the influence of zirconium on the structural organization of soda-lime borosilicate glasses. A new method of quantitative analysis of the ¹⁷O MQMAS spectra is presented, by a direct fit of the two-dimensional MQMAS spectrum which provides the resolution of all the structural groups in glasses containing up to five oxides. Additional data were also obtained from the quantitative deconvolution of the ¹¹B MAS NMR spectra, with the help of the direct fit of MQMAS data as well. Excess of non-bridging oxygen is clearly identified in these glasses. Sixfolded zirconium is preferentially compensated rather than the tetrahedral boron and calcium only partially compensate the tetrahedral boron. Alteration gels arising from glass leaching were probed by oxygen-17 supplied by the alteration solution. Most of the zirconium is inserted in the silicate network forming Si-O-Zr bonds with the same configuration in the glass and in the gel. During leaching, calcium clearly remains in the alteration gel, either near non-bridging oxygen or as a zirconium charge compensator. This quantitative approach applied to ¹⁷O MQMAS spectra demonstrates its potential for investigating the structure of increasingly complex glass and gel compositions.     

Multicomponent synthesis of spiroisoxazolines

A three-component one-pot procedure (3-MCR) was developed to assemble the spiroisoxazoline nucleus from commercially available materials. This new methodology affords the title compounds in high yields and without the use of chromatography.     

Electron density of semi-bridging carbonyls. Metamorphosis of CO ligands observed via experimental and theoretical investigations on [FeCo(CO)(8)](-)

The electron density distribution in a transition-metal dimer containing a semibridging carbonyl is determined through experimental X-ray diffraction and quantum chemical computations. The changes occurring during the evolution from terminal to bridging coordinations are described by a "structure-correlation-like" approach and by a theoretical investigation along the conversion path. The smooth continuum of conformations observed in the solid state is explained in terms of the mutual interplay of direct M-M and M-CO and indirect M- - -M and M- - -C interactions, which can be characterized by interatomic delocalization indexes, within the framework of Quantum Theory of Atoms in Molecules.     

Mass number dependence of the difference (rel−rmu), a dispersion effect in electron scattering

A systematic analysis of rms charge radii determined by elastic electron scattering (r_el) and muonic atom X-rays (r_mu), respectively, shows that — on the average — the former is less then the latter. This difference is probably caused by virtual excitation and deexcitation of the nucleus: a dispersion effect. The mass number dependence of the difference is also investigated. Its absolute value decreases with increasing mass number as (r_el?r_mu)≈ ?12+0.03 A (am). ThisA-dependence is compared with the available theoretical predictions using low-q, low-Z approximations.