Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

Search for new phenomena in events with three charged leptons at a center-of-mass energy of 7 TeV with the ATLAS detector

A generic search for anomalous production of events with at least three charged leptons is presented. The search uses a pp-collision data sample at a center-of-mass energy of root s = 7 TeV corresponding to 4.6 fb(-1) of integrated luminosity collected in 2011 by the ATLAS detector at the CERN Large Hadron Collider. Events are required to contain at least two electrons or muons, while the third lepton may either be an additional electron or muon, or a hadronically decaying tau lepton. Events are categorized by the presence or absence of a reconstructed tau-lepton or Z-boson candidate decaying to leptons. No significant excess above backgrounds expected from Standard Model processes is observed. Results are presented as upper limits on event yields from non-Standard-Model processes producing at least three prompt, isolated leptons, given as functions of lower bounds on several kinematic variables. Fiducial efficiencies for model testing are also provided. The use of the results is illustrated by setting upper limits on the production of doubly charged Higgs bosons decaying to same-sign lepton pairs.

Search for supersymmetry in events with photons, bottom quarks, and missing transverse momentum in proton-proton collisions at a centre-of-mass energy of 7 TeV with the ATLAS detector

A search has been performed for the experimental signature of an isolated photon with high transverse momentum, at least one jet identified as originating from a bottom quark, and high missing transverse momentum. Such a final state may originate from supersymmetric models with gauge-mediated supersymmetry breaking in events in which one of a pair of higgsino-like neutralinos decays into a photon and a gravitino while the other decays into a Higgs boson and a gravitino. The search is performed using the full dataset of 7 TeV proton-proton collisions recorded with the ATLAS detector at the LHC in 2011, corresponding to an integrated luminosity of 4.7 fb(-1). A total of 7 candidate events are observed while 7.5 +/- 2.2 events are expected from the Standard Model background. The results of the search are interpreted in the context of general gauge mediation to exclude certain regions of a benchmark plane for higgsino-like neutralino production.

(Table 1) Biomass (as energy) of different elements of the planktonic community in the Equatorial Pacific in the 0-150 m layer

An analysis was made of composition and content of nutrients, salts, particulate and dissolved organic matter, and various plankton groups in a series of samples collected by a 140-liter sampling bottle to depth up to 150 m at 4 equatorial stations between 97° and 154°W. Large and small phytoplankton, bacteria (aggregated and dispersed), heterotrophic flagellates, infusorians, radiolarians, foraminifers, fine filter-feeders, small and large, mostly herbivorous copepods, cyclopoids, predatory calanoids, and other predators were investigated separately. Trophic relations between these elements are established from personal and published data, and rate of their metabolism and some other physiological parameters are determined. Such functional characteristics as extent of satisfaction of food requirements of organisms belonging to various trophic groups, intensity of trophic relations, balance between production and consumption by individual elements of the community, ecological efficiency, and net and specific production of the groups distinguished, of individual trophic levels, of total zooplankton, and of the community as a whole are calculated. Variations of these characteristics along the equator with decreasing upwelling intensity are examined and their possible causes and mechanisms are discussed.