VITALI-HAHN-SAKS THEOREM FOR VECTOR MEASURES ON OPERATOR ALGEBRAS

We show that the direct generalization of the Vitali–Hahn–Sakstheorem is not valid for all measures on von Neumann algebras.By applying a general equicontinuity argument, we prove a directextension of the Vitali–Hahn–Saks theorem for awide range of vector measures on von Neumann algebra s and JBWalgebras. We also characterize relatively compact sets of vectormeasures on operator algebras.     

Classification of certain subgraphs of the 3‐dimensional grid

We prove by “trial‐ and‐error” that up to isometry, there are exactly four different non‐empty cubic induced subgraphs of the 3‐dimensional grid with girth ≥ 10. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 34–60, 2003     

Synthesis of N-phthalimido β-aminoethanesulfonyl chlorides: the use of thionyl chloride for a simple and efficient synthesis of new peptidosulfonamide building blocks

N-Phthalimido β-aminoethanesulfonyl chlorides, new building blocks for the synthesis of peptidosulfonamide peptidomimetics, were prepared in a straightforward manner from amino acids. In the crucial synthetic step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of refluxing thionyl chloride or thionyl chloride/DMF. This simple and effective chlorinating method is also applicable to β-aminoethane sulfonic acids and their sodium salts with other N-protecting groups.     

Nontrivial application of Nielsen theory to differential systems

In reply to a problem of Jean Leray concerning application of the Nielsen theory to differential systems for obtaining multiplicity results, we present a nontrivial example of such an application. The emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related Hammerstein solution operator. To achieve this goal, we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper-Carathéodory differential inclusions. We are not aware that any alternative approach can be employed, even in the single-valued case.     

On the ideals of equivariant tree models

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group-based models such as the Jukes–Cantor and Kimura models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices. The main novelty is that our results yield generators of the full ideal rather than an ideal which only defines the model set-theoretically. J. Draisma has been supported by DIAMANT, an NWO mathematics cluster and J. Kuttler by an NSERC Discovery Grant.     

Chelating Complexes of Diethylzinc and ZnCl2 with 2,2‐Bipyridine and 1,6,7,12,13,18‐Hexaazatrinaphthylene (HATN) as Ligands

The 1,6,7,12,13,18‐hexaazatrinaphthylene (HATN) complex [(Et₂Zn)₃(μ₃‐HATN)] was synthesized and characterized by IR spectroscopy, UV/Vis spectroscopy, elemental analysis and ESI‐MS spectrometry. Attempts to prepare ZnCl₂ complexes of HATN leads only to the mononuclear [(Cl₂Zn)(HATN)] derivative, characterized by X‐ray diffraction, IR‐ and UV/Vis‐spectroscopy as well as ESI‐MS spectrometry. The bright red 2,2′‐bipyridine (bipy) complex [(Et₂Zn)(bipy)] ( 1 ) was synthesized and characterized by X‐ray diffraction and NMR spectroscopy. The UV/Vis‐spectra of the HATN‐complexes show absorptions in regions of far longer wavelengths than the corresponding 2,2′‐bipyridine or 1,10‐phenantroline complexes. Consequently the π*‐LUMO of HATN ( 5 ) is lower in energy than the π*‐LUMO of 2,2′‐bipyridine ( 2 ) or 1,10‐phenanthroline (phen).     

Determination of starane (fluroxypyr) herbicide using flow injection spectrophotometry.

The starane herbicide was spectrophotometrically determined by the diazotization method in a flow injection assembly. Since starane is a substituted pyridyl compound the NH2 group at the p-position was exploited for diazotization. Starane was diazotized with nitrite and the diazotized product is coupled with beta-naphthol. The absorbance of the resulting azo dye was measured at 395 nm with a molar absorptivity of 1.5 x 10(4) L mol(-1) cm(-1). The calibration graph was linear over the range of 0.6 to 10 microg/mL, with a relative standard deviation (RSD) of 1.67% and a sampling through put of 60 samples h(-1). The % recovery for the determination of starane was found to be 96%. The method was successfully applied to the determination of the active ingredient of starane herbicide in its formulation as well as in food samples.     

Entangled Porphyrins in Cyclodextrin Vesicles

The entanglement process between porphyrins and some amphiphiliccyclodextrins and the occurrence of different species have been proved by the combination of UV-Visabsorption, fluorescence anisotropy, resonance light scattering and ¹H NMR spectroscopy.