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.     

Boundary behavior in Hilbert spaces of vector-valued analytic functions

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions.     

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.     

The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let . Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces.