G-invariante Morse-funktionen

If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory.     

On the gap problem for the sequence ∥mβ∥

We discuss the gap problem for the sequence m used in our previous Letter (D. H. Mayer, Lett. Math. Phys. 16, 139–143 (1988)).     

2-Phosphinophenolate complexes: formation and crystal structure of a novel trinuclear mu-O nickel(II)-tris(P(intersection)O-chelate)

A novel linear trinuclear mu-O-bridging 2-phosphinophenolate nickel(II) complex with fac-tris(P(intersection)O- chelates) in the terminal positions and the three oxygen atoms each facing the central nickel(II) cation was synthesized and structurally characterized by X-ray crystallography. To the best of our knowledge, this is the first example of an octahedral Ni(II) tris(P(intersection)O- chelate).     

Synergies between micropreparative high-performance liquid chromatography and an instrumental optical biosensor

The recent development of an automated surface plasmon resonance technology for the measurement of biomolecular interactions (Pharmacia BIAcore) has provided new opportunities for the detection and analysis of protein-protein interactions. In the BIAcore, detection is based on changes in surface plasmon resonance which are monitored optically. Changes in surface plasmon resonance correspond to changes in surface concentration of macromolecules and can be monitored in real time.

We have found that the detection sensitivity obtainable with this technology (ng/ml concentrations of specific ligands are readily detectable for many applications) is complementary “in a bidirectional manner” to micropreparative HPLC. Thus micropreparative HPLC may be used to purify and characterise reagents for the biosensor, whilst the biosensor may be used to define chromatographic parameters such as elution conditions for affinity chromatography or serve as an affinity detector for fractions obtained during chromatographic purification.

Examples of such applications, including the potential of the biosensor to search for and monitor the purification of unknown ligands for which the target molecule has been identified, are shown. In particular, the use of the biosensor to monitor the purification of soluble epidermal growth factor receptor from A431 cell conditioned media is demonstrated.     

Commutator-finite orthomodular lattices

The class of orthomodular lattices which have only finitely many commutators is investigated. The following theorems are proved: contains the block-finite orthomodular lattices. Every irreducible element of is simple. Every element of is a direct product of a Boolean algebra and finitely many simple orthomodular lattices. The irreducible elements of which are modular, or are M-symmetric with at least one atom, have height two or less.     

Solvent effects on the redox properties of tris-(1,10-phenanthroline)iron(II/III) complexes

The redox properties of the system Fe(tmphen)₃(II/III) (tmphen=3,4,7,8-tetramethyl-1,10-phenanthroline) have been studied in the solvents nitromethane, acetonitrile, propanediol-1,2-carbonate, dimethylformamide, dimethylacetamide, dimethylsulfoxide and of the systems Fe(phen)₃(II/III) (phen=1,10-phenanthroline) and Fe(niphen)₃(II/III) (niphen=5-nitro-1,10-phenanthroline) in the solvents nitromethane, acetonitrile, propanediol-1,2-carbonate and acetone. The redox potentials of Fe(tmphen)₃(II/III) are nearly independent of the solvent suggesting that the system might be used as a reference redox couple similar to the systems ferrocene/ferricinium or bisbiphenylchromium(0/I). In contrast the redox potentials of Fe(niphen)₃(II/III) show a significant decrease with increasing donor number of the solvent which can be explained by nucleophilic attack of solvent molecules at the iron. It is shown that such a mechanism is consistent with the known solvent and salt effects on the kinetics of dissociation of ferroin and ferriin type complexes.     

Sub-microgram-scale analysis by coulometry at controlled potential

The considerations which determine the success of controlled-potential coulometric analyses on the submicrogram level are discussed, and it is shown that the ultimate sensitivity of the method is governed by the accuracy with which the requisite background corrections, especially that for the charging quantity of electricity, can be determined. A method for the coulometric determination of zinc based on these considerations is shown to contain a limiting uncertainty of ± 0.2 mμF_y, so that as little as 0.07 μg of zinc can be determined within about ± 10%, while quantities of zinc exceeding about 10 μg can be determined with an accuracy and precision of ± 0.1% or better. Possible techniques for the further extension of controlled-potential coulometric analysis into the millimicrogram range are briefly discussed.