The zeta function of a simplicial complex

Given a simplicial complex δ on vertices {1, …,n} and a fieldF we consider the subvariety of projective (n−1)-space overF consisting of points whose homogeneous coordinates have support in δ. We give a simple rational expression for the zeta function of this singular projective variety overF _q and show a close connection with the Betti numbers of the corresponding variety over ℂ. This connection is particularly simple in the case when Δ is Cohen-Macaulay.     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

The equivalence problem

The equivalence problem is the problem of deciding whether two metric tensors are related by a coordinate transformation or not. I give a brief historical review of work done on this problem in Stockholm around 1980.     

Solid-phase microextraction for qualitative and quantitative determination of migrated degradation products of antioxidants in an organic aqueous solution

Low molecular weight aromatic substances may migrate out from plastic packaging to their contents, especially if they consist of organic aqueous solutions or oils. It is, therefore, extremely important to be able to identify and quantify any migrated substances in such solutions, even at very low concentrations. We have in this work investigated and evaluated the use of solid-phase microextraction for the specific task of extraction from an organic aqueous solution such as a simulated pharmaceutical solution consisting of 10 vol.% ethanol in water. The goal was furthermore to investigate the possibility of simultaneously identifying and quantifying the substances in spite of differences in their chemical structures. Methods were developed and evaluated for extraction both with direct sampling and with headspace sampling. Difficulties appeared due to the ethanol in the solution and the minute amounts of substances present. We have shown that a simultaneous quantification of migrated low molecular weight degradation products of antioxidants using only one fibre is possible if the extraction method and temperature are adjusted in relation to the concentration levels of the analytes. Comparions were made with solid-phase extraction.     

Controlled Double-Bond Migration in Palladium-Catalyzed Intramolecular Arylation of Enamidines

Palladium-catalyzed intramolecular cyclization of N-(N'-tert-butylformimidoyl)-6-[2-(2-iodophenyl)ethyl]-1,2,3,4-tetrahydropyridine (1a) and N-(N'-tert-butylformimidoyl)-6-[3-(2-iodophenyl)propyl]-1,2,3,4-tetrahydropyridine (1b) respectively results in formation of spiro compounds 1'-(N-tert-butylformimidoyl)-3',4'-dihydrospiro[indan-1,2'(1'H)-pyridine] (4a), 1'-(N-tert-butylformimidoyl)-1',6'-dihydrospiro[indan-1,2'(3'H)-pyridine] (5a), and 1'-(N-tert-butylformimidoyl)-5',6'-dihydrospiro[indan-1,2'(1'H)-pyridine] (6a) and 1'-(N-tert-butylformimidoyl)-3,3',4,4'-tetrahydrospiro[naphthalene-1(2H),2'(1'H)-pyridine] (4b), 1'-(N-tert-butylformimidoyl)-1',3,4,6'-tetrahydrospiro[naphthalene-1(2H),2'(3'H)-pyridine] (5b), and 1'-(N-tert-butylformimidoyl)-3,4,5',6'-tetrahydrospiro[naphthalene-1(2H),2'(1'H)-pyridine] (6b). The double-bond migration process can be controlled, and any of the three double-bond isomers can be prepared by employing proper ligands. A combination of BINAP and the amidine function was required to obtain the isomers 5a and 5b with the double bond in the homoallylic position relative to the aryl group. An electrospray ionization mass spectrometric study was conducted to support suggested reaction intermediates.     

Anionic polymerization of vinyl chloride

Anionic polymerization of vinyl chloride has been studied. Of the organometallic compounds tested as initiators, only butyllithium was found to initiate polymerization. Polymerization in bulk at 0°C and with tert-butyllithium as initiator gave poly(vinyl chloride) in a yield of 38% with M _n = 55,000. Tacticity of the anionic PVC was similar to that of conventional PVC prepared at similar temperatures. Anionic PVC was found to be less branched and more heat-stable than the conventional polymer.     

Mass spectral fragmentation patterns of heterocycles. VI. Carbazole and 1,8-dideuteriocarbazole

The mass spectral fragmentation of carbazole was reinvestigated using metastable ion studies, exact mass measurements and 1,8-dideuteriocarbazole. 1,8-Dideuteriocarbazole was prepared by successive metalations and deuterations of carbazole. The ¹H- and ¹³C-nmr spectra of 1,8-dideuteriocarbazole confirmed earlier assignments for carbazole.     

Separation strategy for acidic chiral pharmaceuticals with capillary electrochromatography on polysaccharide stationary phases

The effect of five factors on the capillary electrochromatographic enantioseparation of acidic compounds was studied using an experimental design. The studied factors were pH, acetonitrile content in the mobile phase, temperature, buffer concentration, and applied voltage. These experiments allowed defining a generic separation strategy applicable on acidic compounds with chemical and structural diversity. The starting screening conditions consist of a 45 mM ammonium formate electrolyte at pH 2.9 mixed with 65% acetonitrile, an applied voltage of 15 kV, and a temperature of 25 degrees C. The screening phase occasionally can be followed by an optimization procedure. Evaluation of the proposed strategy pointed out that it allows achieving baseline resolution within a relatively short time when a beginning of separation is obtained at the starting conditions. This strategy revealed enantioselectivity for 11 compounds out of 15, of which 10 could be baseline-separated after the proposed optimization steps.