The Lamb-dip spectrum of methylcyanide: Precise rotational transition frequencies and improved ground-state rotational parameters

Methylcyanide, CH₃CN, is an important interstellar species, and therefore the accurate knowledge of precise rest frequencies for rotational transitions as well as ground-state rotational and hyperfine constants is needed. In this work the hyperfine structure of the millimeter- and submillimeter-wave spectra of CH₃CN has been further investigated. In addition, accurate THz measurements have been carried out for the first time. Consequently, the present investigation allowed us to provide the most accurate ground state rotational and hyperfine parameters known at the moment for CH₃C¹⁴N. To resolve the hyperfine structure of the rotational transitions observed, the Lamb-dip technique has been exploited. Both frequency-modulated and video-type detections have been employed.     

On a Class of Functionals Whose Local Minima are Global

In this note we introduce a suitable class of functionals, including the class of integral functionals, and prove that any (strict) local minimum of a functional of this class, defined on a decomposable space, is a (strict) global minimum. So, the recent result obtained by Giner in [1] is specified and extended.     

Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Exact solutions inU 4 gravity. I. The ansatz for self double dual curvature

We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U ₄-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.     

Heterocyclic compounds studies. Dynamic 13C NMR investigation and crystal structure of 3-hydroxy-1,5-benzoxathiepine

1-5-benzoxathiepine compounds are a novel class of heterocyclic rings that present interesting properties as central nervous system depressants. With the aim to contribute to the elucidation of the structure-activity relationship of this class of compounds we report a structural study of the 3-hydroxy-1,5-benzoxathiepine both in solution and in the solid state. Studies by dynamic ¹³C-nmr in solution show that three conformations are possible for the oxathiepin ring. A unique chair conformation characterizes the atoms in the oxathiepine ring of the crystallized molecule. The crystal structure was solved by direct methods. Values of bond distances and angles are within the expected range.     

Unimodular lattices with long shadow

Let L be an odd unimodular lattice of dimension n with shadow n−16. If min(L)?3 then dim(L)?46 and there is a unique such lattice in dimension 46 and no lattices in dimensions 44 and 45. To prove this, a shadow theory for theta series with spherical coefficients is developed.     

Structural and spectroscopic studies of silylated cyclo- and bicyclosilanes

A number of cyclo-and bicyclosilanes have been prepared and structurally characterized by X-ray crystallography and Raman spectroscopy. 1,1,4,4- and 1,1,3,3-tetrakis(trimethylsilyl)octamethylcyclohexasilanes were found to exhibit unusual twist- and twisted boat-conformations. The UV absorption properties of all compounds were studied and found to show absorption maxima red shifted compared to the parent compound dodecamethylcyclohexasilane. Dedicated to Prof. Mitsuo Kira on the occasion of his reception of the Wacker Silicon Award 2005 and in recongnition of his numerous outstanding achievements in organosilicon chemistry.