A General Backwards Calculus of Variations via Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-201

Triple oxygen isotopic composition of the high-³He/⁴He mantle

Measurements of Xe isotope ratios in ocean island basalts (OIB) suggest that Earth’s mantle accreted heterogeneously, and that compositional remnants of accretion are sampled by modern, high-3He/4He OIB associated with the Icelandic and Samoan plumes. If so, the high-3He/4He source may also have a distinct oxygen isotopic composition from the rest of the mantle. Here, we test if the major elements of the high-3He/4He source preserve any evidence of heterogeneous accretion using measurements of three oxygen isotopes on olivine from a variety of high-3He/4He OIB locations. To high precision, the Δ17O value of high-3He/4He olivines from Hawaii, Pitcairn, Baffin Island and Samoa, are indistinguishable from bulk mantle olivine (Δ17OBulk Mantle − Δ17OHigh 3He/4He olivine = −0.002 ± 0.004 (2 × SEM)‰). Thus, there is no resolvable oxygen isotope evidence for heterogeneous accretion in the high-3He/4He source. Modelling of mixing processes indicates that if an early-forming, oxygen-isotope distinct mantle did exist, either the anomaly was extremely small, or the anomaly was homogenised away by later mantle convection. The δ18O values of olivine with the highest 3He/4He ratios from a variety of OIB locations have a relatively uniform composition (∼5‰). This composition is intermediate to values associated with the depleted MORB mantle and the average mantle. Similarly, δ18O values of olivine from high-3He/4He OIB correlate with radiogenic isotope ratios of He, Sr, and Nd. Combined, this suggests that magmatic oxygen is sourced from the same mantle as other, more incompatible elements and that the intermediate δ18O value is a feature of the high-3He/4He mantle source. The processes responsible for the δ18O signature of high-3He/4He mantle are not certain, but δ18O–87Sr/86Sr correlations indicate that it may be connected to a predominance of a HIMU-like (high U/Pb) component or other moderate δ18O components recycled into the high-3He/4He source

Fine Root Productivity and Dynamics on a Forested Floodplain in South Carolina

The highly dynamic, fine-root component of forested wetland ecosystems has received inadequate attention in the literature. Characterizing fine root dynamics is a challenging endeavor in any system, but the difficulties are particularly evident in forested floodplains where frequent hydrologic fluctuations directly influence fine root dynamics. Fine root (\u3c 3mm) biomass, production, and turnover were estimated for three soils exhibiting different drainage patterns within a mixed-oak community on the Coosawhatchie River floodplain, Jasper County, SC. Within a 45-cm deep vertical profile, 74% of total fine root biomass was restricted to the upper 15 cm of the soil surface. Fine root biomass decreased as the soil became less well-drained (e.g., fine root biomass in well-drained soil \u3e intermediately drained soil \u3e poorly drained soil). Fine root productivity was measured for one year using minirhizotrons and in-situ screens. Both methods suggested higher fine root production in better drained soils but showed frequent fluctuations in fine root growth and mortality, suggesting the need for frequent sampling at short intervals (e.g., monthly) to accurately assess fine root growth and turnover. Fine root production, estimated with in-situ screens, was 1.5, 1.8, and 0.9 Mg ha-1 yr-1 in the well-drained, intermediately drained, and poorly drained soils, respectively. Results from minirhizotrons indicated that fine roots in well-drained soils grew to greater depths while fine roots in poorly drained soils were restricted to surface soils. Minirhizotrons also revealed that the distribution of fine roots among morphological classes changed between well-drained and poorly drained soils

Transverse Momentum in Semi-Inclusive Polarized Deep Inelastic Scattering and the Spin-Flavor Structure of the Proton

The non-valence spin-flavor structure of the nucleon extracted from semi-inclusive measurements of polarized deep inelastic scattering depends strongly on the transverse momentum of the detected hadrons which are used to determine the individual polarized sea distributions. This physics may explain the recent HERMES observation of a positively polarized strange sea through semi-inclusive scattering, in contrast to the negative strange sea polarization deduced from inclusive polarized deep inelastic scattering.Comment: 4 pages, revtex style, 2 figure

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models

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

Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS

We present the results of a search for new, heavy particles that decay at a significant distance from their production point into a final state containing charged hadrons in association with a high-momentum muon. The search is conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS detector operating at the Large Hadron Collider. Production of such particles is expected in various scenarios of physics beyond the standard model. We observe no signal and place limits on the production cross-section of supersymmetric particles in an R-parity-violating scenario as a function of the neutralino lifetime. Limits are presented for different squark and neutralino masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final version to appear in Physics Letters

Measurement of the inclusive isolated prompt photon cross-section in pp collisions at sqrt(s)= 7 TeV using 35 pb-1 of ATLAS data

A measurement of the differential cross-section for the inclusive production of isolated prompt photons in pp collisions at a center-of-mass energy sqrt(s) = 7 TeV is presented. The measurement covers the pseudorapidity ranges |eta|<1.37 and 1.52<=|eta|<2.37 in the transverse energy range 45<=E_T<400GeV. The results are based on an integrated luminosity of 35 pb-1, collected with the ATLAS detector at the LHC. The yields of the signal photons are measured using a data-driven technique, based on the observed distribution of the hadronic energy in a narrow cone around the photon candidate and the photon selection criteria. The results are compared with next-to-leading order perturbative QCD calculations and found to be in good agreement over four orders of magnitude in cross-section.Comment: 7 pages plus author list (18 pages total), 2 figures, 4 tables, final version published in Physics Letters