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.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

Photodynamic therapy of human glioma spheroids using 5-aminolevulinic acid

The response of human glioma spheroids to 5-aminolevulinic acid (ALA)-mediated photodynamic therapy (PDT) is investigated. A two-photon fluorescence microscopy technique is used to show that human glioma cells readily convert ALA to protoporphyrin IX throughout the entire spheroid volume. The central finding of this study is that the response of human glioma spheroids to ALA-mediated PDT depends not only on the total fluence, but also on the rate at which the fluence is delivered. At low fluences (< or = 50 J cm-2), lower fluence rates are more effective. At a fluence of 50 J cm-2, near-total spheroid kill is observed at fluence rates of as low as 10 mW cm-2. The fluence rate effect is not as pronounced at higher fluences (> 50 J cm-2), where a favorable response is observed throughout the range of fluence rates investigated. The clinical implications of these findings are discussed.     

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.     

Experimental tests of the feasibility of singlet oxygen luminescence monitoring in vivo during photodynamic therapy

Singlet oxygen (1O2) is thought to be the cytotoxic agent in photodynamic therapy (PDT) with current photosensitizers. Direct monitoring of 1O2 concentration in vivo would be a valuable tool in studying biological response. Attempts were made to measure 1O2 IR luminescence during PDT of cell suspensions and two murine tumour models using the photosensitizers Photofrin II and aluminium chlorosulphonated phthalocyanine. Instrumentation was virtually identical to that devised by Parker in the one positive report of in vivo luminescence detection in the literature. Despite the fact that our treatments caused cell killing and tissue necrosis, we were unable to observe 1O2 emission under any conditions. We attribute this negative result to a reduction in 1O2 lifetime in the cellular environment. Quantitative calibration of our system allowed us to estimate that the singlet oxygen lifetime in tissue is less than 0.5 microsecond. Some technical improvements are suggested which would improve detector performance and perhaps make such measurements feasible.     

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.