Filament sets and homogeneous continua

New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.     

Temperature dependence of the configurational free energy of a branched polymer

We consider a lattice model of branched polymers in dilute solution in which the polymer is modelled as an animal, weakly embeddable in the (simple cubic) lattice. In order to model the effect on the thermodynamic properties of changing the temperature or the quality of the solvent, we include an energy associated with the number of nearneighbour contacts between pairs of vertices of the animals. We show that the configurational free energy of the animal is a continuous function of the temperature and derive rigorous upper and lower bounds on the temperature dependence of the free energy. Finally, we comment on similarities between these results and corresponding ones for a model in which the energy is associated with the cyclomatic index of the animal.     

Entangled polymers in condensed phases

We present Monte Carlo results on a model of polymers in a condensed phase, over a range of monomer densities. We imagine cutting a cube out of the system. This cube will typically have several polymer molecules running through its interior, and starting and ending on the boundary. These subchains will be mutually entangled and we present a way to assess the extent of entanglement complexity as a function of the monomer density and the number of subchains in the cube. The model is a set of k self-avoiding and mutually avoiding walks, properly embedded in the cube.     

Entanglement complexity of lattice ribbons

We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as n, and similar results hold for the twist and writhe.     

Optical properties of human prostate at 732 nm measured in mediated photodynamic therapy

Characterization of the tissue light penetration in prostate photodynamic therapy (PDT) is important to plan the arrangement and weighting of light sources so that sufficient light fluence is delivered to the treatment volume. The optical properties (absorption [mu(a)], transport scattering [mu(s)'] and effective attenuation [mu(eff)] coefficients) of 13 patients with locally recurrent prostate cancer were measured in situ using interstitial isotropic detectors. Measurements were made at 732 nm before and after motexafin lutetium (MLu)-mediated PDT in four quadrants. Optical properties were derived by applying the diffusion theory to the fluence rates measured at several distances (0.5-5 cm) from a point source. mu(a) and mu(s)' varied between 0.07 and 1.62 cm(-1) (mean 0.37 +/- 0.24 cm(-1)) and 1.1 and 44 cm(-1) (mean 14 +/- 11 cm(-1)), respectively. mu(a) was proportional to the concentration of MLu measured by an ex vivo fluorescence assay. We have observed, on average, a reduction of the MLu concentration after PDT, presumably due to the PDT consumption of MLu. mu(eff) varied between 0.91 and 6.7 cm(-1) (mean 2.9 +/- 0.7 cm(-1)), corresponding to an optical penetration depth (delta = 1/micro(eff)) of 0.1-1.1 cm (mean 0.4 +/- 0.1 cm). The mean penetration depth at 732 nm in human prostate is at least two times smaller than that found in normal canine prostates, which can be explained by a four times increase of the mean value of mu(s)' in human prostates. The mean light fluence rate per unit source strength at 0.5 cm from a point source was 1.5 +/- 1.1 cm(-2), excluding situations when bleeding occurs. The total number of measurements was N = 121 for all mean quantities listed above. This study showed significant inter- and intraprostatic differences in the optical properties, suggesting that a real-time dosimetry measurement and feedback system for monitoring light fluences during treatment should be considered for future PDT studies.     

Component B binding to the soluble methane monooxygenase hydroxylase by saturation-recovery EPR spectroscopy of spin-labeled MMOB

Spin-labeled Cys89 of the soluble methane monooxygenase regulatory protein (MMOB) from Methylococcus capsulatus (Bath) binds within 15 +/- 4 A of the hydroxylase (MMOH) diiron center, placing the MMOB docking site in the MMOH "canyon" region on iron-coordinating helices E and F of the alpha-subunit.     

Inclusion complex formation of β-cyclodextrin and Naproxen: a study on exothermic complex formation by differential scanning calorimetry

Inclusion complex formation between β-cyclodextrin and Naproxen was investigated using differential scanning calorimetry (DSC) as a function of the β-cyclodextrin-to-Naproxen molar ratio, ranging from 0:5:1 to 5:1. When these mixtures are heated above the melting temperature of Naproxen, an exothermic peak is observed at a temperature slightly higher than the melting peak of Naproxen. This peak, which has not been previously reported, has been interpreted as an exothermic energy of inclusion complex formation. The magnitude of this complex formation peak was found to be dependent upon the composition of the β-cyclodextrin and Naproxen mixture and increased in magnitude to a maximum value at a β-cyclodextrin:Naproxen molar ratio of 2:1. In addition, Naproxen recrystallization and re-melting peaks seen in the cooling and re-heating scans, respectively, decreased in magnitude with increasing molar ratio and totally disappeared for the mixture with 5:1 of β-cyclodextrin to Naproxen ratio indicative of complete inclusion of Naproxen in the cyclodextrin cavities. Complete inclusion was further reflected by the disappearance of key Naproxen peaks in Fourier transform infrared spectra of samples recovered from DSC experiments. The large excess of β-cyclodextrin needed to fully complex the Naproxen was found to be due to slow kinetics. Increasing the hold time after the initial melting led to inclusion efficiencies up to 95 % even for the 2:1 mixture. These experiments suggest that ratios of β-cyclodextrin:Naproxen 2:1 or greater facilitate the process by increasing the presence of cyclodextrin molecules in the close proximity of the drug molecules and lead to high inclusion efficiencies.     

Self-avoiding Walks and Polymer Adsorption: Low Temperature Behaviour

We give a brief review of the self-avoiding walk model of polymer adsorption highlighting some open problems in the area. We then discuss the low temperature behaviour and derive some results about the behaviour of the free energy at low temperatures.     

Filament sets, aposyndesis, and the decomposition theorem of Jones

Applications of the work introduced by the authors in a recent article, Filament sets and homogeneous continua, are given to aposyndesis and local connectedness. The aposyndetic decomposition theorem of Jones is generalized to spaces with the property of Kelley.

     

Some current issues in accounting for the cost of defined benefit pension schemes

This paper discusses the issues underlying the InternationalAccounting Standards Board (IASB)'s review of accounting forpension obligations. Pension obligations are currently dealtwith by International Accounting Standard 19. This containsthree important features, which are currently under review:(1) A smoothing mechanism (the ‘corridor’) for recognizingactuarial gains and losses. (2) An expected rate of return onplan assets, which is different from the actual (achieved) return.(3) An asset ceiling, which limits the extent to which surplusplan assets are recognized in the accounts of the employer.The IASB's current thinking on these issues is explained, andcomparisons are made with the UK's controversial Financial ReportingStandard 17. The paper concludes with a brief discussion oftwo important aspects of measuring defined benefit obligationsthat are not being considered in the present review.