26 Science Research Writing of soft surfaces have previously been studied and attributed to the mechanical properties of the sample (Weisenhorn et al., 1992; Radmacher et al., 1993, 1995; Hoh and Schoenenberger, 1994). However thin samples such as two-dimensional protein arrays or biological membranes adsorbed to a solid support are not suffi ciently compressible to explain such large height variation. Here we demonstrate that electrostatic interactions between the AFM tip and the sample (Butt, 1991a, b) infl uence the measured height of a biological structure adsorbed to a solid support in buff er solution. Th e DLVO (Derjaguin, Landau, Verwey, Overbeek) theory (Israelachvili, 1991) is used to describe the electrostatic repulsion and van der Waals attraction acting between tip and sample (Butt et al., 1995). Experimental results and calculations show that the electrostatic double-layer forces can be eliminated by adjusting the electrolyte concentration (Butt, 1992a, b), providing conditions for correct height measurements with the AFM. In addition, the observed height dependence of the biological structure on electrolyte concentration allows its surface charge density to be estimated. Optimal location discrimination of two multipartite pure states 1. INTRODUCTION Entanglement lies at the heart of many aspects of quantum information theory and it is therefore desirable to understand its structure as well as possible. One attempt to improve our understanding of entanglement is the study of our ability to perform information theoretic tasks locally on non-local states, such as the local implementation of non-local quantum gates [2], telecloning [3], the remote manipulation and preparation of quantum states [4] or the recently studied question of the local discrimination of non-local states by a variety of authors. In [1] it was shown that any two orthogonal pure states can be perfectly discriminated locally, whereas in [5] examples of two orthogonal mixed states were presented which cannot be distinguished
Introduction — Writing Task 27 perfectly locally. Another surprising development is that there exist bases of product orthogonal pure states which cannot be locally reliably discriminated, despite the fact that each state in the basis contains no entanglement [6]. Here we discuss the issue of discriminating two non-orthogonal pure states locally, and show that in this regime the optimal global procedure can be achieved. Inert COD production in a membrane anaerobic reactor treating brewery wastewater INTRODUCTION Th e chemical characterization of wastewaters is commonly undertaken to determine their biological treatability, load on an existing treatment system, or compliance with the fi nal discharge standards. In each case, one of the most important parameters to be measured is the chemical oxygen demand (COD). In general, the COD value of a wastewater mainly represents the biodegradable and non-biodegradable organic components, although inorganic compounds may be signifi cant in certain cases. In biological treatment systems, the biodegradable fraction of wastewater can be removed eff ectively, but its non-biodegradable fraction passes through the system unchanged. In addition to this, a signifi cant amount of soluble microbial products may be produced by microorganisms within the treatment systems. Some of these will be resistant to biological degradation and will appear in reactor effl uents. Th e factors that aff ect effl uent quality and overall organic matter removal in biological treatment systems are, therefore, the presence of both the inert COD fraction in the infl uent wastewater and the soluble microbial products which are produced during biological treatment. Although their concentrations may have few practical implications in the treatment of low strength wastewaters, they may have relatively greater signifi cance in the treatment of medium-high strength industrial wastewaters. Th ere is extensive literature on the determination of inert COD fractions in industrial wastewaters under aerobic conditions (Chudoba, 1985; Ekama et al., 1986; Rittman et al., 1987;