The diophantine equation y2 + K = x3

The effective method of Baker is applied to the equation y2 = x3 - 28 and all integral solutions are found.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34194/1/0000483.pd

Carbon on the Northwest European Shelf: Contemporary Budget and Future Influences

© Copyright © 2020 Legge, Johnson, Hicks, Jickells, Diesing, Aldridge, Andrews, Artioli, Bakker, Burrows, Carr, Cripps, Felgate, Fernand, Greenwood, Hartman, Kröger, Lessin, Mahaffey, Mayor, Parker, Queirós, Shutler, Silva, Stahl, Tinker, Underwood, Van Der Molen, Wakelin, Weston and Williamson. A carbon budget for the northwest European continental shelf seas (NWES) was synthesized using available estimates for coastal, pelagic and benthic carbon stocks and flows. Key uncertainties were identified and the effect of future impacts on the carbon budget were assessed. The water of the shelf seas contains between 210 and 230 Tmol of carbon and absorbs between 1.3 and 3.3 Tmol from the atmosphere annually. Off-shelf transport and burial in the sediments account for 60–100 and 0–40% of carbon outputs from the NWES, respectively. Both of these fluxes remain poorly constrained by observations and resolving their magnitudes and relative importance is a key research priority. Pelagic and benthic carbon stocks are dominated by inorganic carbon. Shelf sediments contain the largest stock of carbon, with between 520 and 1600 Tmol stored in the top 0.1 m of the sea bed. Coastal habitats such as salt marshes and mud flats contain large amounts of carbon per unit area but their total carbon stocks are small compared to pelagic and benthic stocks due to their smaller spatial extent. The large pelagic stock of carbon will continue to increase due to the rising concentration of atmospheric CO2, with associated pH decrease. Pelagic carbon stocks and flows are also likely to be significantly affected by increasing acidity and temperature, and circulation changes but the net impact is uncertain. Benthic carbon stocks will be affected by increasing temperature and acidity, and decreasing oxygen concentrations, although the net impact of these interrelated changes on carbon stocks is uncertain and a major knowledge gap. The impact of bottom trawling on benthic carbon stocks is unique amongst the impacts we consider in that it is widespread and also directly manageable, although its net effect on the carbon budget is uncertain. Coastal habitats are vulnerable to sea level rise and are strongly impacted by management decisions. Local, national and regional actions have the potential to protect or enhance carbon storage, but ultimately global governance, via controls on emissions, has the greatest potential to influence the long-term fate of carbon stocks in the northwestern European continental shelf

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of the Lambda(b) cross section and the anti-Lambda(b) to Lambda(b) ratio with Lambda(b) to J/Psi Lambda decays in pp collisions at sqrt(s) = 7 TeV

The Lambda(b) differential production cross section and the cross section ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/Psi Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and Lambda to proton pion, using a data sample corresponding to an integrated luminosity of 1.9 inverse femtobarns. The product of the cross section times the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls faster than that of b mesons. The measured value of the cross section times the branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06 +/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively.Comment: Submitted to Physics Letters

Search for new physics in events with opposite-sign leptons, jets, and missing transverse energy in pp collisions at sqrt(s) = 7 TeV

A search is presented for physics beyond the standard model (BSM) in final states with a pair of opposite-sign isolated leptons accompanied by jets and missing transverse energy. The search uses LHC data recorded at a center-of-mass energy sqrt(s) = 7 TeV with the CMS detector, corresponding to an integrated luminosity of approximately 5 inverse femtobarns. Two complementary search strategies are employed. The first probes models with a specific dilepton production mechanism that leads to a characteristic kinematic edge in the dilepton mass distribution. The second strategy probes models of dilepton production with heavy, colored objects that decay to final states including invisible particles, leading to very large hadronic activity and missing transverse energy. No evidence for an event yield in excess of the standard model expectations is found. Upper limits on the BSM contributions to the signal regions are deduced from the results, which are used to exclude a region of the parameter space of the constrained minimal supersymmetric extension of the standard model. Additional information related to detector efficiencies and response is provided to allow testing specific models of BSM physics not considered in this paper.Comment: Replaced with published version. Added journal reference and DO

Measurement of isolated photon production in pp and PbPb collisions at sqrt(sNN) = 2.76 TeV

Isolated photon production is measured in proton-proton and lead-lead collisions at nucleon-nucleon centre-of-mass energies of 2.76 TeV in the pseudorapidity range |eta|<1.44 and transverse energies ET between 20 and 80 GeV with the CMS detector at the LHC. The measured ET spectra are found to be in good agreement with next-to-leading-order perturbative QCD predictions. The ratio of PbPb to pp isolated photon ET-differential yields, scaled by the number of incoherent nucleon-nucleon collisions, is consistent with unity for all PbPb reaction centralities.Comment: Submitted to Physics Letters

Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

Peer reviewe

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

Peer reviewe