From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.This research was partially supported by MINECO of Spain, grant MTM2011-29064-C03-02, and by the NAFOSTED of Vietnam

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one

Observation of the diphoton decay of the Higgs boson and measurement of its properties

Peer reviewe

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV

Peer reviewe

Study of double parton scattering using W+2-jet events in proton-proton collisions at √s=7 TeV

Peer reviewe

Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at √s=8 Tev

Peer reviewe

Measurement of Higgs boson production and properties in the WW decay channel with leptonic final states

Peer reviewe

Measurements of the tt¯ charge asymmetry using the dilepton decay channel in pp collisions at √s=7 TeV

Peer reviewe

Measurement of the production cross section ratio σ(χb2(1P))/σ(χb1(1P))in pp collisions at √s=8TeV

A measurement of the production cross section ratio σ(χb2(1P))/σ(χb1(1P))σ(χb2(1P))/σ(χb1(1P)) is presented. The χb1(1P)χb1(1P) and χb2(1P)χb2(1P) bottomonium states, promptly produced in pp collisions at View the MathML sources=8 TeV, are detected by the CMS experiment at the CERN LHC through their radiative decays χb1,2(1P)→ϒ(1S)+γχb1,2(1P)→ϒ(1S)+γ. The emitted photons are measured through their conversion to e+e−e+e− pairs, whose reconstruction allows the two states to be resolved. The ϒ(1S)ϒ(1S) is measured through its decay to two muons. An event sample corresponding to an integrated luminosity of 20.7 fb−120.7 fb−1 is used to measure the cross section ratio in a phase-space region defined by the photon pseudorapidity, |ηγ|<1.0|ηγ|<1.0; the ϒ(1S)ϒ(1S) rapidity, |yϒ|<1.5|yϒ|<1.5; and the ϒ(1S)ϒ(1S) transverse momentum, View the MathML source7<pTϒ<40 GeV. The cross section ratio shows no significant dependence on the ϒ(1S)ϒ(1S) transverse momentum, with a measured average value of View the MathML source0.85±0.07(stat+syst)±0.08(BF), where the first uncertainty is the combination of the experimental statistical and systematic uncertainties and the second is from the uncertainty in the ratio of the χbχb branching fractions