The Hodge Filtration and Cyclic Homology

We relate the Hodge filtration of the cohomology of a complex algebraic variety X to the Hodge decomposition of its cyclic homology. If X is smooth and projective, is the quotient of the Betti cohomology by the piece of the Hodge filtration.     

Ethynyloxirane anions: a new tool for natural product synthesis

Ethynyl oxiranes can be deprotonated with nBuLi in THF and trapped with various electrophiles, providing a stereoselective access to trisubstituted oxiranes. Alkyl iodides and aldehydes react readily with the ethynyloxiranyl anions but not sulfonyl derivatives. Mechanistic investigations highlighted the stabilizing role of the ethynyl group, the localization of the anion and the coordinating role of the oxirane oxygen atom during deprotonation.     

Bass’ NK groups and cdh-fibrant Hochschild homology

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ?, we describe K _*(R[t])/K _*(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass’ question, whether K _n (R)=K _n (R[t]) implies K _n (R)=K _n (R[t ₁,t ₂]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.     

Die Bestimmung des Kohlenstoffs im Stahl nach direkten physikalischen Verfahren)

Ohne Zusammenfassung     

The Higher K-Theory of Real Curves

If X is a smooth curve defined over the real numbers , we show that K _n (X) is the sum of a divisible group and a finite elementary Abelian 2-group when n 2. We determine the torsion subgroup of K _n (X), which is a finite sum of copies of and 2, only depending on the topological invariants of X() and X(), and show that (for n 2) these torsion subgroups are periodic of order 8.     

Engineering of highly luminescent lanthanide tags suitable for protein labeling and time-resolved luminescence imaging

The synthesis of a new ligand LH(4) based on a glutamic acid skeleton bis-functionalized on its nitrogen atom by 6-methylene-6'-carboxy-2,2'-bipyridine chromophoric units is described. UV-vis spectrophotometric titrations revealed the formation of 1:1 M:L complexes with lanthanide(III) cations, and complexation of LH(4) with equimolar amounts of hydrated LnCl(3) salts (Ln = Eu, Gd, and Tb) gave water-soluble and stable complexes of the general formula [LnL(H(2)O)]Na, which were characterized by elemental analysis, IR, UV-vis absorption spectroscopy, (1)H NMR (Ln = Eu), and mass spectrometry. The conditional stability constant for formation of the [EuL(H(2)O)]Na complex was determined by competitive complexation experiments to be log K = 16.5 +/- 0.6 in 0.01 M TRIS/HCl buffer (pH = 7.0). In water solution, the [EuL(H(2)O)]Na and [TbL(H(2)O)]Na complexes were highly luminescent with quantum yields of 8% and 31%, respectively, despite the presence of ca. one water molecule in the first coordination sphere of the metal ions. Activation of the appended carboxylate function of the glutamate moiety in the form of an N-hydroxysuccinimidyl ester allows for the covalent linking of the complexes to primary amino groups of biological compounds. Bovine serum albumin (BSA) was labeled with both Eu or Tb complexes, and the Ln-BSA conjugates were characterized by UV-vis absorption and emission spectroscopy and MALDI-TOF mass spectrometry. Labeling ratios (number of complex molecules per BSA) of ca. 8:1 and 7:1 were established for Eu-BSA and Tb-BSA, respectively. The suitability of the tagged compound for use in bioanalytical time-resolved luminescence microscopy was established by comparison with fluorescein-labeled probes.