Continued fractions and transcendental numbers

It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains arbitrarily large partial quotients. Apparently, this question was first considered by Khintchine. A preliminary step towards its resolution consists in providing explicit examples of transcendental continued fractions. The main purpose of the present work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to new combinatorial transcendence criteria recently obtained by Adamczewski and Bugeaud

Large-Q^2 behavior of the pion electromagnetic form factor

We study the large-Q^2 behavior of the electromagnetic form factor of the pion, which is viewed as a quark-antiquark bound state in a (nongauge) quantum field theory. When the pion's Bethe-Salpeter wave function is expanded in O(4) partial waves, it is found that the information needed about the partial-wave amplitudes is their scaling behavior at large momentum and the locations of their poles in the complex J plane. This information is determined by using the operator-product expansion, conformal invariance at short distances, and a regularity property that holds at least in the ladder model. The resulting behavior of the form factor is roughly F(Q^2)~(Q^2)^(-1), with corrections due to anomalous dimensions

An expressed sequence tag survey of gene expression in the pond snail Lymnaea stagnalis, an intermediate vector of Fasciola hepatica

The pond snail Lymnaea stagnalis is an intermediate vector for the liver fluke Fasciola hepatica, a common parasite of ruminants and humans. Yet, despite being a disease of medical and economic importance, as well as a potentially useful comparative tool, the genetics of the relationship between Lymnaea and Fasciola has barely been investigated. As a complement to forthcoming F. hepatica expressed sequence tags (ESTs), we generated 1320 ESTs from L. stagnalis central nervous system (CNS) libraries. We estimate that these sequences derive from 771 different genes, of which 374 showed significant similarity to proteins in public databases, and 169 were similar to ESTs from the snail vector Biomphalaria glabrata. These L. stagnalis ESTs will provide insight into the function of the snail CNS, as well as the molecular components of behaviour and response to parasitism. In the future, the comparative analysis of Lymnaea/Fasciola with Biomphalaria/Schistosoma will help to understand both conserved and divergent aspects of the host-parasite relationship. The L. stagnalis ESTs will also assist gene prediction in the forthcoming B. glabrata genome sequence. The dataset is available for searching on the world-wide web at http://zeldia.cap.ed.ac.uk/mollusca.html

Through the Grapevine: New Developments in the Protection of Geographical Indications in China

26 pagesChina is one of the fastest growing markets for wine consumption, on track to move from the fifth to the second largest consumer of wine in the world in the next five years. While the per capita consumption in China pales in comparison to countries like France and the United States, the massive population of over 1.3 billion people means that even slight growth in per capita consumption translates to tremendous growth in overall consumption

Cold water aquifer storage

A working prototype system is described in which water is pumped from an aquifer at 70 F in the winter time, chilled to a temperature of less than 50 F, injected into a ground-water aquifer, stored for a period of several months, pumped back to the surface in the summer time. A total of 8.1 million gallons of chilled water at an average temperature of 48 F were injected. This was followed by a storage period of 100 days. The recovery cycle was completed a year later with a total of 8.1 million gallons recovered. Approximately 20 percent of the chill energy was recovered

Exercise redox biochemistry:conceptual, methodological and technical recommendations

Exercise redox biochemistry is of considerable interest owing to its translational value in health and disease. However, unaddressed conceptual, methodological and technical issues complicate attempts to unravel how exercise alters redox homeostasis in health and disease. Conceptual issues relate to misunderstandings that arise when the chemical heterogeneity of redox biology is disregarded which often complicate attempts to use redox-active compounds and assess redox signalling. Further, that oxidised macromolecule adduct levels reflect formation and repair is seldom considered. Methodological and technical issues relate to the use of out-dated assays and/or inappropriate sample preparation techniques that confound biochemical redox analysis. After considering each of the aforementioned issues, we outline how each issue can be resolved and provide a unifying set of recommendations. We specifically recommend that investigators: consider chemical heterogeneity, use redox-active compounds judiciously, abandon flawed assays, carefully prepare samples and assay buffers, consider repair/metabolism, use multiple biomarkers to assess oxidative damage and redox signalling

Light-cone behavior of the pion Bethe-Salpeter wave function in the ladder model

The Bethe-Salpeter wave function χ(q^ν+P^ν, q^ν) for two spin-½ quarks bound by the exchange of a scalar meson is examined in the ladder model. We seek the behavior of χ as the squared momentum, (q+P)^2, on one leg becomes infinite while the squared momentum, q^2, on the other leg remains fixed. This behavior is investigated by making a Wick rotation, expanding χ in partial-wave amplitudes χ^i_J(q^2) of the group O(4), and then looking for the rightmost poles of χ^i_J(q^2) in the complex J plane. Our results verify (in the ladder model) the useful hypothesis that the locations of these poles are independent of q^2 and can thus be computed in the q^2→∞ limit by using conformal invariance

Following microscopic motion in a two dimensional glass-forming binary fluid

The dynamics of a binary mixture of large and small discs are studied at temperatures approaching the glass transition using an analysis based on the topology of the Voronoi polygon surrounding each atom. At higher temperatures we find that dynamics is dominated by fluid-like motion that involves particles entering and exiting the nearest-neighbour shells of nearby particles. As the temperature is lowered, the rate of topological moves decreases and motion becomes localised to regions of mixed pentagons and heptagons. In addition we find that in the low temperature state particles may translate significant distances without undergoing changes in their nearest neig hbour shell. These results have implications for dynamical heterogeneities in glass forming liquids.Comment: 12 pages, 7 figure

On the use of linear-elastic local stresses to design load-carrying fillet-welded steel joints against static loading

This paper uses local linear-elastic stresses to estimate the static strength of steel arc welded joints. The proposed design methodology was developed by taking as a starting point the fundamental concepts on which the Theory of Critical Distances (TCD) is based. The overall accuracy of the devised approach was checked against a number of experimental results taken from the literature and generated by testing a variety of welded geometries. Such a systematic validation exercise demonstrated that the TCD is highly accurate in estimating the static strength of arc welded joints irrespective of the complexity of the assessed welded detail’s geometry