Symmetries and constants of the motion for singular Lagrangian systems

A classification of infinitesimal symmetries of singular autonomous and nonautonomous Lagrangian systems is obtained. The relationship between infinitesimal symmetries and constants of the motion is given.     

On the use of x-ray-excited optical luminescence (XEOL) for the analysis of multisite rare-earth systems

The realization of a XEOL (X-ray-excited optical luminescence) spectrometer is reported. The aim of the present paper is to show that a comparison between UV-excited emission spectra and XEOL spectra can be helpful in the assignment of some weak transitions for multiple site rare-earth compounds. The case of c-Y₂O₃ doped with Eu³⁺ cations is considered in some detail, as in the XEOL spectrum three lines to be assigned to transitions occurring at the centrosymmetrical Eu³⁺ (C_3i) site are strongly enhanced. Additional site-selective UV-excited emission spectra are also reported supporting the present discussion.     

On a site-selective exafs experiment using optical emission

X-ray-excited optical luminescence (XEOL) is known to offer an alternative detection scheme of EXAFS spectra. Although this secondary emission appears restricted to a rather limited number of systems, we show that it can afford, under appropriate circumstances, an interesting property of site selectivity. The case of a ZnO + ZnTPP mixture was chosen as an illustrative example. The relevant formulation of the phenomenon for powdered samples is developed and the requirements for site selectivity are discussed.     

A diversity-oriented strategy for the construction of tetrasubstituted pyrroles via coupled domino processes

A new microwave-assisted rearrangement of 1,3-oxazolidines scaffolds is the basis for a new, metal-free, direct, and modular construction of tetrasubstituted pyrroles from terminal-conjugated alkynes, aldehydes, and primary amines. This new reaction manifold entails two linked domino processes in a one-pot manner with both atom- and bond-efficiency and under very simple and environment-friendly experimental conditions.     

1,3-Diyl trapping reactions. Fundamental investigations with application to the synthesis of linearly fused tricyclopentanoids

A comparison of the inter- and intramolecular diyl trapping routes to linearly fused tricyclopentanoids is presented. In addition, several of the factors which are responsible for the stereoselectivity which is associated with the intramolecular process are examined and it is concluded that conformational rather than electronic (secondary orbital) factors play the dominant role. It is shown that gem methyl groups located on the acyclic chain which joins the diyl and diylophile (in reference to 32 and 35, but not to 47) have no practical effect upon the outcome of the trapping reaction. The intramolecular process is stereospecific with respect to diylophile geometry, and highly stereoselective with respect to the ring junction stereochemistry. Finally, an abortive attempt to synthesize the marine natural product Δ⁹⁽¹²)-capnellene (19) as well as a successful synthesis of the mold metabolite d,l- hirsutene (18) is presented.     

On the closed graph theorem in topological spaces

In this paper we introduce the class of C-Suslin topological spaces and we study some properties of this class in relation to the closed graph theorem.