Effect of oxygen content on the specific heat and magnetic susceptibility of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript>

The specific heat and magnetic susceptibility of a sample of YBa₂Cu₃O_7?δ (YBCO) was measured for 0≤δ≤0.85, 0.8≤T≤120K, and H=0, 3, 5, 7, 9T. The data show the existence of both S=1/2 and S=2 paramagnetic centers, consistent with EPR results. The δ dependences of their concentrations and of other parameters are reported.     

The empirical behavior of sampling methods for stochastic programming

We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant 9726385. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant DMS-0073770. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grants 9726385 and 0082065.     

Decoherence Functionals for von Neumann Quantum Histories: Boundedness and Countable Additivity

Gell–Mann and Hartle have proposed a significant generalisation of quantum theory in which decoherence functionals perform a key role. Verifying a conjecture of Isham–Linden–Schreckenberg, the author analysed the structure of bounded, finitely additive, decoherence functionals for a general von Neumann algebra A (where A has no Type I₂ direct summand). Isham et al. had already given a penetrating analysis for the situation where A is finite dimensional. The assumption of countable additivity for a decoherence functional may seem more plausible, physically, than that of boundedness. The results of this note are obtained much more generally but, when specialised to L(H), the algebra of all bounded linear operators on a separable Hilbert space H, give: Let d be a countably additive decoherence functional defined on all pairs of projections in L(H). If H is infinite dimensional then d must be bounded. By contrast, when H is finite dimensional, unbounded (countably additive) decoherence functionals always exist for L(A). Received: 6 December 1996 / Accepted: 18 May 1997     

Anisotropy and temperature dependence of small angle neutron scattering from silicon-oxide precipitates in silicon

Czochralski grown silicon crystals contain interstitially dissolved oxygen which diffuses on heating to form precipitates of silica. We have examined these precipitates by small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.4 Å^–1. The obtained SANS patterns reveal pronounced anisotropic intensity distributions which resemble the symmetry of the host crystal. The SANS spectra show an anisotropic central peak at Q<0.1 Å^–1 due to the single particle shape and a number of weak intensities for larger Q-values. These weak side maxima are considered correlation peaks or quasi-elastic interference peaks. They show, however, an unexpected and distinct temperature dependence: with decreasing temperature below values of 220 K their intensity is lost slowly, but reversibly. At T = 50 K only the central peak from the single-particle scattering remains unchanged. Upon heating, the correlation peaks regain their former value of intensity and Q-position without any evidence of thermal hysteresis.     

A Fair Allocation of County Cricket Opponents

Each team in the English County Cricket Championship plays against some other teams twice a year, and others only once. This paper describes a case study whose aim was to overcome this inherent unfairness by producing a four-year schedule of opponents which was as fair as possible, and could be easily seen to be fair, while still allowing for traditional rivalries. The schedule also needed to be satisfactory in regard to several other constraints and objectives. Various simple heuristics were used; these are described in some detail. Of particular interest is the effectiveness of a ‘local non-worsening’ approach when the objective is to find any feasible solution. This is equivalent to simulated annealing at a constant temperature of absolute zero.     

The coarse Baum–Connes conjecture via coarse geometry

The C₀ coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C₀ version of the coarse Baum–Connes conjecture and show that K_*(C^*X₀) is a topological invariant for a broad class of metric spaces. Using this result we construct a ‘geometric’ obstruction group to the coarse Baum–Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum–Connes conjecture in this context.     

Matrix Effects on Selective Chemical Sensing by Sol-Gel Entrapped Complexing Agents

Changes in the selectivity of molecular recognition systems on sol-gel entrapment are reported. Thermodynamic effects are exemplified by studies of the metal-ion complexing agent Eriochrome Cyanine R (ECR). In aqueous solution this binds strongly and selectively to Al3+, whereas in a TMOS-based sol-gel matrix it is selective for Cu3+. Thermodynamic effects, due to restricted translational freedom of water molecules or different solvent structure and isolation of ligands, can explain these observations. Effects of entrapment on molecular recognition by a large conformationally flexible molecule have been studied using a tris-terminated PAMAM dendrimer. The dendrimer conformation and its complexation with Cu2+ changes on entrapment, and binding of aromatic carboxylic acids such as ibuprofen can be detected by changes in visible absorption and surface plasmon resonance using spun films of the sol-gel composite. These effects show that in addition to providing a porous entrapment matrix of good optical quality, sol-gels may be used to alter the binding characteristics of the entrapped receptors.