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

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

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

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

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

Embodying the therapeutic alliance : an exploration of the working alliance in the personal trainer-client relationship

This quasi-experimental study examines, from the standpoint of the personal trainer, the extent to which the working alliance and its component parts of goal, task and bond as defined within Bordin\u27s (1975, 1979) theoretical framework, are experienced in the working relationship between personal trainer and client. Additionally, the study explores whether a personal trainer\u27s or a client\u27s ethnicity or gender, a trainer\u27s age or training history, the frequency of the personal training sessions, or the length of the training relationship impact the working alliance total or its subscale scores. An anonymous online survey was distributed by email to several hundred personal trainers. The survey included demographic information about the personal trainer, questions about the personal training client and length and frequency of the training relationship, and the Working Alliance Inventory - Short Revised Therapist-rated version (WAI-SRT-G). After data collection was complete, the sample consisted of 94 nationally-certified personal trainers, aged 21 years or older, who trained at least 50% of their clients in a gym setting. The major findings of the study were 1.) The mean total alliance and subscale scores reflected the presence of a strong working alliance. 2.) The bond subscales scores had the highest mean. 3.) When total alliance and subscale scores were compared by gender or ethnicity of personal trainer or client, no significant differences were found. 4.) Significant differences in total alliance and in certain subscales were found across the number of weekly training sessions and the personal trainers\u27 years of experienc

A 24/7 Public Possession: Understanding the Dissonance and Grace of Being a Post- Secondary Leader

This study explores the perspectives and understandings of post-secondary leaders and their contexts as described through the qualitative experiences of 12 Maritime Canadian leaders (presidents and vice-presidents) who work in contemporary, publicly funded, post-secondary institutions. Four themes emerge: balancing daily dissonance, learning experientially to lead, creating learning spaces, and needing moments of grace. The research reveals that leaders seek deeper understandings of their work and their characterization.  Cette étude explore les perspectives et les connaissances de leaders en éducation postsecondaire et leurs contextes, tels que décrits par le biais des expériences qualitatives de 12 leaders (présidents et vice-présidents) canadiens des provinces des Maritimes qui œuvrent dans des établissements d’enseignement postsecondaires contemporains et publics. Quatre thèmes ressortent de l’étude : l’équilibre de la dissonance quotidienne, l’apprentissage expérimental pour devenir leader, la création de lieux d’apprentissage et le besoin de vivre des moments de grâce. La recherche révèle que les leaders aspirent à une compréhension plus approfondie de leur travail et de l’interprétation que l’on en fait