Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems

We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic centre manifolds. We assume that the unperturbed system has an orbit connecting a hyperbolic fixed point on one centre manifold to a hyperbolic fixed point on the other. Then we prove some old and new results concerning the persistence of these connecting orbits and apply the results to find examples of systems in dimensions greater than three which possess Sil’nikov saddle-focus homoclinic orbits.Розглянуто сингулярно збурену систему, що залежить вiд двох параметрiв та має два (можливо, однаковi) нормально гiперболiчнi центрованi многовиди. При цьому припускається, що незбурена система має орбiту, яка поєднує гiперболiчну нерухому точку на одному центрованому многовидi з гiперболiчною нерухомою точкою на iншому. Доведено деякi вiдомi та новi результати щодо збереження цих орбiт та наведено приклади систем розмiрностi бiльше, нiж три, що мають сiдловi фокуснi гомоклiнiчнi орбiти Сiльнiкова

Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

Temperature and Photoperiod Effects on Sterility in a Cytoplasmic Male-Sterile Soybean

Manual cross-pollination to produce large quantities of hybrid soybean seed is difficult and time consuming. An environmentally stable sterility system is one of the necessary components to produce large quantities of hybrid seed. The objective of this study was to subject cytoplasmic male-sterile (CMS) BC5F1 plants, from a cross of a Chinese Glycine max wild-type soybean with a Chinese wild annual soybean G. soja (male parent) and controls, to a variety of different temperature and photoperiod treatments to test whether CMS is stable under various environmental conditions. Plants were grown in growth chambers under controlled temperature, photoperiod, and irradiance regimes until pod set, and then they were transferred to a glasshouse until they matured. Plants were evaluated for time of anthesis after photoperiod induction (13 h light/11 h dark) and fertility or sterility. Anther squash and pod set data showed that sterility of the CMS line was stable under all environmental conditions tested, whereas fertility-restored control plants remained fertile. Extreme environmental conditions led to delayed floral induction and/or stunted growth

Outbreak of Neisseria meningitidis capsular group W among scouts returning from the World Scout Jamboree, Japan, 2015

The 23rd World Scout Jamboree was held in Japan from 28 July to 8 August 2015 and was attended by over 33,000 scouts from 162 countries. An outbreak of invasive meningococcal disease capsular group W was investigated among participants, with four confirmed cases identified in Scotland, who were all associated with one particular scout unit, and two confirmed cases in Sweden; molecular testing showed the same strain to be responsible for illness in both countries. The report describes the public health action taken to prevent further cases and the different decisions reached with respect to how wide to extend the offer of chemoprophylaxis in the two countries; in Scotland, chemoprophylaxis was offered to the unit of 40 participants to which the four cases belonged and to other close contacts of cases, while in Sweden chemoprophylaxis was offered to all those returning from the Jamboree. The report also describes the international collaboration and communication required to investigate and manage such multinational outbreaks in a timely manner

Automated dynamic thermal simulation of houses and housing stocks using readily available reduced data

This paper describes a new method to swiftly model the dynamics of heating energy demand and indoor air temperatures of houses and housing stocks. The Reduced data Energy Model (RdDEM) provides a cost-effective alternative to steady-state modelling by enhancing the input dataset from the Reduced data Standard Assessment Procedure (RdSAP) – the method used to calculate Energy Performance Certificates (EPC) in the UK. This eliminates the main drawbacks associated with dynamic thermal simulation (DTS) of housing stocks, namely the large amount of required input data and the significant time required to model each house. The RdDEM algorithms create RdSAP-equivalent geometry, construction, thermal mass and boundary conditions in Energy Plus DTS software. The new inferences and methodological enhancements were first tested and then implemented at scale using a sample of 83 semi-detached houses. Most energy results from RdDEM were within 10% of those from RdSAP. The differences are explained by the different ways that indoor air temperature is calculated. The RdDEM method provides a dynamic alternative to RdSAP for understanding the dynamics of energy demand and indoor air temperatures in homes. This could include assessing the peak demand of a community energy scheme or assessing the summertime overheating risk in individual dwellings. Ultimately, it could provide a dynamic housing stock model using the data already collected from millions of houses to generate EPCs

The Complete Nucleotide Sequence of the Coffee (Coffea Arabica L.) Chloroplast Genome: Organization and Implications for Biotechnology and Phylogenetic Relationships Amongst Angiosperms

The chloroplast genome sequence of Coffea arabica L., the first sequenced member of the fourth largest family of angiosperms, Rubiaceae, is reported. The genome is 155 189 bp in length, including a pair of inverted repeats of 25 943 bp. Of the 130 genes present, 112 are distinct and 18 are duplicated in the inverted repeat. The coding region comprises 79 protein genes, 29 transfer RNA genes, four ribosomal RNA genes and 18 genes containing introns (three with three exons). Repeat analysis revealed five direct and three inverted repeats of 30 bp or longer with a sequence identity of 90% or more. Comparisons of the coffee chloroplast genome with sequenced genomes of the closely related family Solanaceae indicated that coffee has a portion of rps19 duplicated in the inverted repeat and an intact copy of infA. Furthermore, whole-genome comparisons identified large indels (\u3e 500 bp) in several intergenic spacer regions and introns in the Solanaceae, including trnE (UUC)–trnT (GGU) spacer, ycf4–cemA spacer, trnI (GAU) intron and rrn5–trnR (ACG) spacer. Phylogenetic analyses based on the DNA sequences of 61 protein-coding genes for 35 taxa, performed using both maximum parsimony and maximum likelihood methods, strongly supported the monophyly of several major clades of angiosperms, including monocots, eudicots, rosids, asterids, eurosids II, and euasterids I and II. Coffea (Rubiaceae, Gentianales) is only the second order sampled from the euasterid I clade. The availability of the complete chloroplast genome of coffee provides regulatory and intergenic spacer sequences for utilization in chloroplast genetic engineering to improve this important crop

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter