Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Synthesis,magnetic and spectral studies of iron(III) and cobalt(II,III) complexes of 4-formylantipyrine N(4)-substituted thiosemicarbazones

The synthesis and characterization of complexes of iron(III), cobalt(II) and cobalt(III) with 4-formylantipyrine N(4)-methyl-, N(4)-dimethyl-, and 3-piperidylthiosemicarbazones are reported. Elemental analyses, molar conductivities, magnetic measurements and spectral (i.r., electronic and e.s.r.) studies have been used to elucidate the nature of the metal complexes. The i.r. spectra show that the thiosemicarbazones behave as bidentate or tridentate ligands, either in the thione or thiolato form. Different stereochemistries are proposed for the various cobalt(II) complexes on the basis of spectral and magnetic studies. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formation of nitrogen‐containing heterocycles using di(imidazole‐1‐yl)methanimine

A mild and efficient synthesis of five‐ and six‐membered nitrogen containing heterocyclic compounds, in which di(imidazole‐1‐yl)methanimine serves as a one‐carbon source, is reported.     

LAMMA mass spectra of β-diketone,bis(benzoylacetone)ethylenediimine and bis(salicylidene)ethylenediimine complexes of some transition metals

Complexes of 2,4-pentanedione (acetylacetone, acac), [Cu(acac)₂], [VO(acac)₂] and [CO(acac)₃], and the chromium(III) derivative of 3-methyl-2,4-pentanedione (methylacetylacetone, meac), [Cr(meac)₃], the ligands bis(benzoylacetone)ethylenediimine and bis(salicylidene)ethylenediimine, and their cobalt(II), nickel(II) and copper(II) chelates were analysed by laser desorption mass spectrometry (LAMMA) and compared to electron impact (EI) results. The positive ion LAMMA spectra generally reveal mostly small fragments, although metal cationization peaks are seen for most complexes. Negative ion LAMMA produce carbon clusters and some structurally important fragments.     

Synthesis and photolysis of doxyl derivatives of 5β-androstan-3-ones

In an unsuccessful attempt to effect remote functionalization at C9, 4,4-dimethyloxazolidine-N-oxyl (doxyl) derivatives at C3 of 5β-androstan-3,17-dione and 5β-androstan-17β-ol-3-one were prepared and photolyzed. The former doxyl yielded its C13 stereoisomer; the latter was converted very slowly to intractable material.     

A copper-catalyzed C-N bond formation involving sp-hybridized carbons. A direct entry to chiral ynamides via N-alkynylation of amides

A copper-catalyzed new C-N bond formation involving a sp-hybridized carbon is described here leading to a facile entry for syntheses of chiral ynamides. This direct N-alkynylation of amides should have a significant impact on the future development of synthetic methodologies employing ynamides.     

Structures of lanthanide shift reagent complexes by molecular mechanics computations

Molecular mechanics calculations have been applied to the structure determination of 7-coordinate lanthanide complexes. To circumvent problems in defining oxygen—lanthanide—oxygen bond angles, the energy of angle deformations at the metal center are not evaluated explicitly. Instead the standard approach to molecular mechanics calculations is modified by including 1,3-nonbonded interactions between atoms that are both bonded to the metal center. Geometry optimization for two known lanthanide complexes afforded structures that are in reasonable agreement with X-ray crystal structures, and small discrepancies are attributed to cyrstal packing forces.     

Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.