On topological extensions of Archimedean and non-Archimedean rings

The usage of the fields of p-adic numbers Q _p , rings of m-adic numbers Q _m and more general ultrametric rings in theoretical physics induced the interest to topological-algebraic studies on topological extensions of rational and real numbers and more generally (commutative and even noncommutative) rings. It is especially interesting to investigate a possibility to proceed to non-Archimedean rings by starting with real numbers. In particular, in this note we present “no-go” theorems (Theorems 3, 4) by which one cannot obtain an ultrametric ring by extending (in a natural way) the ring of real numbers. This puremathematical result has some interest for non-Archimedean physics: to explore ultrametricity one has to give up with the real numbers — to work with rings of e.g. m-adic numbers (where m > 1 is a natural, may be nonprime, number).     

Hecke correspondences for smooth moduli spaces of sheaves

Publications mathématiques de l'IHÉS - We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and...     

Chiral recognition in solution and the gas phase. Experimental and theoretical studies of aromatic D- and L-amino acid–Cu(II)–chiragen complexes Jennifer L. Seymour František Tureček Andrei V. Malkov Pavel Kočovský Journal of Mass Spectrometry 2004; 39: 1044–1052

The original article to which this Erratum refers was published in Journal of Mass Spectrometry 2004; 39: 1044–1052.     

Synthesis, X-ray diffraction studies, and DFT calculations on hexacoordinated germanium derivatives: the case of germaspirobis(ocanes)

Synthesis of the title compounds, viz. [RN(CH2CHR'O)2]2Ge (1, R = Me, R' = H; 2, R = Me, R' = Ph; 3, R = Ph, R' = H), by the reaction of 2 equiv of corresponding dialkanolamines RN(CH2CHR'OH)2 (4, R = Me, R' = H; 5, R = Me, R' = Ph; 6, R = Ph, R' = H) with (AlkO)4Ge is reported. Composition and structures of all novel compounds were established by 1H and 13C NMR spectroscopy and mass spectrometry as well as elemental analysis data. The single-crystal X-ray diffraction of 2 has clearly indicated the presence of two transannular interactions Ge<--N in the compound. N atoms are cis-orientated. The compound 3 possesses long Ge...N distances. The structural data obtained from geometry optimizations by DFT calculations on 1-3 reproduces experimental results. Both cis- and trans-isomers were studied, and cis-configuration was found to be more thermodynamically stable for all three compounds. The transition states for possible cis <--> trans rearrangement processes in 1-3 were calculated. The properties of the Ge-O and Ge<--N bonds in 1-3 were analyzed by the AIM approach. The interactions between the Ge atom and N atoms as well as O atoms possess predominantly ionic character.     

Synthesis and Structural Characterisation of Two Copper(II) Complexes of <Emphasis Type="Italic">N</Emphasis>-(1-acetyl-2-propylidene) (2-pyridylmethyl) amine

Two new complexes [CuBr(C₁₁H₁₃N₂O)] (1) and [Cu(NCO)(C₁₁H₁₃N₂O)] (2) containing the tridentate Schiff base ligand, N-(1-acetyl-2-propylidene)(2-pyridylmethyl) amine which is the 1:1 condensation product of acetylacetone and 2-aminomethylpyridine, have been synthesised and characterised by elemental analysis, IR and electronic spectra, electrochemical study and single crystal X-ray diffraction study. Crystal structures reveal that the copper atom in both the complexes are in square geometry formed by the N₂O donor set of the Schiff base and a bromine atom in 1 and one cyanate ligand in 2. Both bromide and isocyanate ligands act in a terminal monodentate fashion.