Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

Good practice in reviewing and publishing studies on herbal medicine, with special emphasis on traditional Chinese medicine and Chinese materia medica

Ethnopharmacological relevance: Studies on traditional Chinese medicine (TCM), like those of other systems of traditional medicine (TM), are very variable in their quality, content and focus, resulting in issues around their acceptability to the global scientific community. In an attempt to address these issues, an European Union funded FP7 consortium, composed of both Chinese and European scientists and named “Good practice in traditional Chinese medicine” (GP-TCM), has devised a series of guidelines and technical notes to facilitate good practice in collecting, assessing and publishing TCM literature as well as highlighting the scope of information that should be in future publications on TMs. This paper summarises these guidelines, together with what has been learned through GP-TCM collaborations, focusing on some common problems and proposing solutions. The recommendations also provide a template for the evaluation of other types of traditional medicine such as Ayurveda, Kampo and Unani. Materials and methods: GP-TCM provided a means by which experts in different areas relating to TCM were able to collaborate in forming a literature review good practice panel which operated through e-mail exchanges, teleconferences and focused discussions at annual meetings. The panel involved coordinators and representatives of each GP-TCM work package (WP) with the latter managing the testing and refining of such guidelines within the context of their respective WPs and providing feedback. Results: A Good Practice Handbook for Scientific Publications on TCM was drafted during the three years of the consortium, showing the value of such networks. A “deliverable – central questions – labour division” model had been established to guide the literature evaluation studies of each WP. The model investigated various scoring systems and their ability to provide consistent and reliable semi-quantitative assessments of the literature, notably in respect of the botanical ingredients involved and the scientific quality of the work described. This resulted in the compilation of (i) a robust scoring system and (ii) a set of minimum standards for publishing in the herbal medicines field, based on an analysis of the main problems identified in published TCM literature.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0