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.     

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.     

Theory usage and theoretical trends in Europe: a survey and preliminary analysis of CERME4 research reports

The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4^th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports¹ on theory usage by European researchers inseven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance on ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner's vision of bridging theoretical traditions which are independently formulated in different regions of the world.