A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Models and metaphors: complexity theory and through-life management in the built environment

Complexity thinking may have both modelling and metaphorical applications in the through-life management of the built environment. These two distinct approaches are examined and compared. In the first instance, some of the sources of complexity in the design, construction and maintenance of the built environment are identified. The metaphorical use of complexity in management thinking and its application in the built environment are briefly examined. This is followed by an exploration of modelling techniques relevant to built environment concerns. Non-linear and complex mathematical techniques such as fuzzy logic, cellular automata and attractors, may be applicable to their analysis. Existing software tools are identified and examples of successful built environment applications of complexity modelling are given. Some issues that arise include the definition of phenomena in a mathematically usable way, the functionality of available software and the possibility of going beyond representational modelling. Further questions arising from the application of complexity thinking are discussed, including the possibilities for confusion that arise from the use of metaphor. The metaphor of a 'commentary machine' is suggested as a possible way forward and it is suggested that an appropriate linguistic analysis can in certain situations reduce perceived complexity

Erasmus Language students in a British University – a case study

Students’ assessment of their academic experience is actively sought by Higher Education institutions, as evidenced in the National Student Survey introduced in 2005. Erasmus students, despite their growing numbers, tend to be excluded from these satisfaction surveys, even though they, too, are primary customers of a University. This study aims to present results from bespoke questionnaires and semi-structured interviews with a sample of Erasmus students studying languages in a British University. These methods allow us insight into the experience of these students and their assessment as a primary customer, with a focus on language learning and teaching, university facilities and student support. It investigates to what extent these factors influence their levels of satisfaction and what costs of adaptation if any, they encounter. Although excellent levels of satisfaction were found, some costs affect their experience. They relate to difficulties in adapting to a learning methodology based on a low number of hours and independent learning and to a guidance and support system seen as too stifling. The results portray this cohort’s British University as a well-equipped and well-meaning but ultimately overbearing institution, which may indicate that minimising costs can eliminate some sources of dissatisfaction

Assessment of New Hub-and-spoke and Point-to-point Airline Network Configurations

This paper aims to provide new measures of airline network configuration with a view to analyse effectively the complexity of modern carriers' network design. It studies network configurations in the airline sector by taking into account both spatial and temporal dimensions. The spatial dimension is measured by using both the Gini index and the Freeman index, which originate from social science research. The temporal dimension is measured by the connectivity ratio, i.e. the share of indirect connections over the total number of connections. According to these indicators, the configuration of the largest full-service carriers and the largest low-cost carriers in Europe is investigated. The results show that the temporal dimension provides a clear distinction between full-service carriers and low-cost carriers; while the spatial dimension appears useful when identifying the peculiarities within groups

Evidence for the Rare Decay B -> K*ll and Measurement of the B -> Kll Branching Fraction

We present evidence for the flavor-changing neutral current decay $B\to K^*\ell^+\ell^-$ and a measurement of the branching fraction for the related process $B\to K\ell^+\ell^-$, where $\ell^+\ell^-$ is either an $e^+e^-$ or $\mu^+\mu^-$ pair. These decays are highly suppressed in the Standard Model, and they are sensitive to contributions from new particles in the intermediate state. The data sample comprises $123\times 10^6$ $\Upsilon(4S)\to B\bar{B}$ decays collected with the Babar detector at the PEP-II $e^+e^-$ storage ring. Averaging over $K^{(*)}$ isospin and lepton flavor, we obtain the branching fractions ${\mathcal B}(B\to K\ell^+\ell^-)=(0.65^{+0.14}_{-0.13}\pm 0.04)\times 10^{-6}$ and ${\mathcal B}(B\to K^*\ell^+\ell^-)=(0.88^{+0.33}_{-0.29}\pm 0.10)\times 10^{-6}$, where the uncertainties are statistical and systematic, respectively. The significance of the $B\to K\ell^+\ell^-$ signal is over $8\sigma$, while for $B\to K^*\ell^+\ell^-$ it is $3.3\sigma$.Comment: 7 pages, 2 postscript figues, submitted to Phys. Rev. Let

Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions

The weak nucleon axial-vector form factor for quasi-elastic interactions is determined using neutrino interaction data from the K2K Scintillating Fiber detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of which half are charged-current quasi-elastic interactions nu-mu n to mu- p occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for oxygen and assume the form factor is approximately a dipole with one parameter, the axial vector mass M_A, and fit to the shape of the distribution of the square of the momentum transfer from the nucleon to the nucleus. Our best fit result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated vector form factors from recent electron scattering experiments and a discussion of the effects of the nucleon momentum on the shape of the fitted distributions.Comment: 14 pages, 10 figures, 6 table

Measurement of Branching Fraction and Dalitz Distribution for B0->D(*)+/- K0 pi-/+ Decays

We present measurements of the branching fractions for the three-body decays B0 -> D(*)-/+ K0 pi^+/-$and their resonant submodes$B0 -> D(*)-/+ K*+/- using a sample of approximately 88 million BBbar pairs collected by the BABAR detector at the PEP-II asymmetric energy storage ring. We measure: B(B0->D-/+ K0 pi+/-)=(4.9 +/- 0.7(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K0 pi+/-)=(3.0 +/- 0.7(stat) +/- 0.3 (syst)) 10^{-4} B(B0->D-/+ K*+/-)=(4.6 +/- 0.6(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K*+/-)=(3.2 +/- 0.6(stat) +/- 0.3 (syst)) 10^{-4} From these measurements we determine the fractions of resonant events to be : f(B0-> D-/+ K*+/-) = 0.63 +/- 0.08(stat) +/- 0.04(syst) f(B0-> D*-/+ K*+/-) = 0.72 +/- 0.14(stat) +/- 0.05(syst)Comment: 7 pages, 3 figures submitted to Phys. Rev. Let

Metabolic evolution and the self-organization of ecosystems

Metabolism mediates the flow of matter and energy through the biosphere. We examined how metabolic evolution shapes ecosystems by reconstructing it in the globally abundant oceanic phytoplankter Prochlorococcus To understand what drove observed evolutionary patterns, we interpreted them in the context of its population dynamics, growth rate, and light adaptation, and the size and macromolecular and elemental composition of cells. This multilevel view suggests that, over the course of evolution, there was a steady increase in Prochlorococcus' metabolic rate and excretion of organic carbon. We derived a mathematical framework that suggests these adaptations lower the minimal subsistence nutrient concentration of cells, which results in a drawdown of nutrients in oceanic surface waters. This, in turn, increases total ecosystem biomass and promotes the coevolution of all cells in the ecosystem. Additional reconstructions suggest that Prochlorococcus and the dominant cooccurring heterotrophic bacterium SAR11 form a coevolved mutualism that maximizes their collective metabolic rate by recycling organic carbon through complementary excretion and uptake pathways. Moreover, the metabolic codependencies of Prochlorococcus and SAR11 are highly similar to those of chloroplasts and mitochondria within plant cells. These observations lead us to propose a general theory relating metabolic evolution to the self-amplification and self-organization of the biosphere. We discuss the implications of this framework for the evolution of Earth's biogeochemical cycles and the rise of atmospheric oxygen.Simons Foundation (Grant SCOPE 329108)Gordon and Betty Moore Foundation (Grant 3778)Gordon and Betty Moore Foundation (Grant 495.01

Formation of the ηc\eta_c in Two-Photon Collisions at LEP

The two-photon width $\Gamma_{\gamma\gamma}$ of the $\eta_c$ meson has been measured with the L3 detector at LEP. The $\eta_c$ is studied in the decay modes $\pi^+\pi^-\pi^+\pi^-$, $\pi^+\pi^-$K$^+$K$^-$, K$_s^0$K$^\pm\pi^\mp$, K$^+$K$^-\pi^{0}$, $\pi^+\pi^-\eta$, $\pi^+\pi^-\eta'$, and $\rho^+\rho^-$ using an integrated luminosity of 140 pb$^{-1}$ at $\sqrt{s} \simeq 91$ GeV and of 52 pb$^{-1}$ at $\sqrt{s} \simeq 183$ GeV. The result is $\Gamma_{\gamma\gamma}(\eta_c) = 6.9 \pm 1.7 (stat.) \pm 0.8 (sys.) \pm 2.0$(BR) keV. The $Q^2$ dependence of the $\eta_c$ cross section is studied for $Q^2 < 9$ GeV$^{2}$. It is found to be better described by a Vector Meson Dominance model form factor with a J-pole than with a $\rho$-pole. In addition, a signal of $29 \pm 11$ events is observed at the $\chi_c0$ mass. Upper limits for the two-photon widths of the $\chi_c0$, $\chi_c2$, and $\eta_c'$ are also given