A note on boundary conditions for nonlinear operators

We investigate boundary conditions for strict-$\psi$-contractive and $\psi$-condensing operators. We derive results on the existence of eigenvectors with positive and negative eigenvalues and we obtain fixed point theorems for classes of noncompact opera\-tors.

Optimal retraction problem for proper $k$-ball-contractive mappings in $C^m [0,1]$

In this paper for any $\varepsilon >0$ we construct a new proper $k$-ball-contractive retraction of the closed unit ball of the Banach space $C^m [0,1]$ onto its boundary with $k < 1+ \varepsilon$, so that the Wośko constant $W_\gamma (C^m [0,1])$ is equal to $1$.

Proper 1-ball contractive retractions in Banach spaces of measurable functions

In this paper we consider the Wosko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k > 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct. 1. Introduction Let X be an infinite-dimensional Banach space with unit closed ball B(X) and unit sphere S(X). It is well known that, in this setting, there is a retraction of B(X) onto S(X), that is, a continuous mapping R : B(X) ! S(X) with Rx = x for all x 2 S(X). In (4) Benyamini and Sternf…

HΛ3 and H‾Λ¯3 production in Pb–Pb collisions at sNN=2.76 TeV

Abstract The production of the hypertriton nuclei H Λ 3 and H ‾ Λ ¯ 3 has been measured for the first time in Pb–Pb collisions at s NN = 2.76  TeV with the ALICE experiment at LHC. The p T -integrated H Λ 3 yield in one unity of rapidity, d N / d y × B . R . ( H Λ 3 → He 3 , π − ) = ( 3.86 ± 0.77 ( stat. ) ± 0.68 ( syst. ) ) × 10 − 5 in the 0–10% most central collisions, is consistent with the predictions from a statistical thermal model using the same temperature as for the light hadrons. The coalescence parameter B 3 shows a dependence on the transverse momentum, similar to the B 2 of deuterons and the B 3 of 3He nuclei. The ratio of yields S 3 = H Λ 3 / ( He 3 × Λ / p ) was measured to b…

Transverse momentum spectra and nuclear modification factors of charged particles in pp, p-Pb and Pb-Pb collisions at the LHC

We report the measured transverse momentum ($p_{\rm T}$) spectra of primary charged particles from pp, p-Pb and Pb-Pb collisions at a center-of-mass energy $\sqrt{s_{\rm NN}} = 5.02$ TeV in the kinematic range of $0.15<p_{\rm T}<50$ GeV/$c$ and $|\eta|< 0.8$. A significant improvement of systematic uncertainties motivated the reanalysis of data in pp and Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV, as well as in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV, which is also presented. Spectra from Pb-Pb collisions are presented in nine centrality intervals and are compared to a reference spectrum from pp collisions scaled by the number of binary nucleon-nucleon collisions. For cent…

Dielectron and heavy-quark production in inelastic and high-multiplicity proton–proton collisions at s=13TeV

The measurement of dielectron production is presented as a function of invariant mass and transverse momentum (pT) at midrapidity (|ye|&lt;0.8) in proton–proton (pp) collisions at a centre-of-mass energy of s=13 TeV. The contributions from light-hadron decays are calculated from their measured cross sections in pp collisions at s=7 TeV or 13 TeV. The remaining continuum stems from correlated semileptonic decays of heavy-flavour hadrons. Fitting the data with templates from two different MC event generators, PYTHIA and POWHEG, the charm and beauty cross sections at midrapidity are extracted for the first time at this collision energy: dσcc¯/dy|y=0=974±138(stat.)±140(syst.)±214(BR)μb and dσbb…

Charged jet cross section and fragmentation in proton-proton collisions at √s = 7 TeV

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. We report the differential charged jet cross section and jet fragmentation distributions measured with the ALICE detector in proton-proton collisions at a center-of-mass energy √s=7  TeV. Jets with pseudorapidity |η|40  GeV/c, the pythia calculations also agree with the measured charged jet cross section. pythia6 simulations describe the fragmentation distributions to 15%. Larger discrepancies are observed for pythia8. SCOAP

Rearrangement and convergence in spaces of measurable functions

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to th…

The ALICE Transition Radiation Detector: Construction, operation, and performance

The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron identification and triggering, the TRD also contributes significantly to the track reconstruction and calibration in the central barrel of ALICE. In this paper the design, construction, operation, and performance of this detector are discussed. A pion rejection factor of up to 410 is achieved at a momentum of 1 GeV/$c$ in p-Pb collisions and the resolution at high transverse momentum improves by about 40% when including the TRD information in track reconstruction. The triggering capability is demonstrated both …

Searches for transverse momentum dependent flow vector fluctuations in Pb-Pb and p-Pb collisions at the LHC

The measurement of azimuthal correlations of charged particles is presented for Pb-Pb collisions at $\sqrt{s_{\rm NN}}=$ 2.76 TeV and p-Pb collisions at $\sqrt{s_{\rm NN}}=$ 5.02 TeV with the ALICE detector at the CERN Large Hadron Collider. These correlations are measured for the second, third and fourth order flow vector in the pseudorapidity region $|��|&lt;0.8$ as a function of centrality and transverse momentum $p_{\rm T}$ using two observables, to search for evidence of $p_{\rm T}$-dependent flow vector fluctuations. For Pb-Pb collisions at 2.76 TeV, the measurements indicate that $p_{\rm T}$-dependent fluctuations are only present for the second order flow vector. Similar results hav…

Inclusive quarkonium production at forward rapidity in pp collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {\sqrt{s}=8}~$$\end{document}s=8TeV

We report on the inclusive production cross sections of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{J}/\psi }$$\end{document}J/ψ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\psi (\mathrm{2S})}$$\end{document}ψ(2S), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepac…

An extension of Guo's theorem via k--contractive retractions

Abstract Let X be a infinite-dimensional Banach space. We generalize Guo's Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k- ψ -contractions and condensing mappings, under a condition which depends on the infimum k ψ of all k ⩾ 1 for which there exists a k- ψ -contractive retraction of the closed unit ball of the space X onto its boundary.

Eigenvectors of k–ψ-contractive wedge operators

AbstractWe present new boundary conditions under which the fixed point index of a strict-ψ-contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k–ψ-contractive wedge operators.

Real-time data processing in the ALICE High Level Trigger at the LHC

At the Large Hadron Collider at CERN in Geneva, Switzerland, atomic nuclei are collided at ultra-relativistic energies. Many final-state particles are produced in each collision and their properties are measured by the ALICE detector. The detector signals induced by the produced particles are digitized leading to data rates that are in excess of 48 GB/$s$. The ALICE High Level Trigger (HLT) system pioneered the use of FPGA- and GPU-based algorithms to reconstruct charged-particle trajectories and reduce the data size in real time. The results of the reconstruction of the collision events, available online, are used for high level data quality and detector-performance monitoring and real-tim…

Search for a common baryon source in high-multiplicity pp collisions at the LHC

Physics letters / B B811, 135849 (2020). doi:10.1016/j.physletb.2020.135849

Eigenvectors of k-psi-contractive wedge operators

We present new boundary conditions under which the fixed point index of a strict-$\psi$-contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k-$\psi$-contractive wedge operators.

On Boundary Conditions for Wedge Operators on Radial Sets

We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.

Dielectron production in proton-proton and proton-lead collisions at √sNN=5.02TeV

The first measurements of dielectron production at midrapidity (|ηe| &lt; 0.8) in proton–proton and proton–lead collisions at √sNN = 5.02 TeV at the LHC are presented. The dielectron cross section is measured with the ALICE detector as a function of the invariant mass mee and the pair transverse momentum pT, ee in the ranges mee &lt; 3.5 GeV/c2 and pT, ee &lt; 8 GeV/c, in both collision systems. In proton–proton collisions, the charm and beauty cross sections are determined at midrapidity from a fit to the data with two different event generators. This complements the existing dielectron measurements performed at √s = 7 and 13 TeV. The slope of the √s dependence of the three measurements is…

Production of K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{*}$$\end{document}∗(892)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{0}$$\end{document}0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}ϕ(1020) in p–Pb collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s_{{\text {NN}}}}$$\end{document}sNN = 5.02 TeV

The production of K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{*}$$\end{document}∗(892)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{0}$$\end{document}0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage…

Direct photon production in Pb–Pb collisions atsNN=2.76 TeV

Direct photon production at mid-rapidity in Pb–Pb collisions at √sNN = 2.76 TeV was studied in the transverse momentum range 0.9<pT<14 GeV/c. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the ALICE detector material with the e+e− pair reconstructed in the central tracking system. The results of the two methods were combined and direct photon spectra were measured for the 0–20%, 20–40%, and 40–80% centrality classes. For all three classes, agreement was found with perturbative QCD calculations for pT≳5 GeV/c. Direct photon spectra down to pT≈1 GeV/c could be extracted for the 20–40% and 0–20% centrality classes. The significance of th…

Kaon femtoscopy in Pb-Pb collisions at √sNN=2.76 TeV

We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at √ s NN = 2.76 TeV. Femtoscopy is used to measure the space-time characteristics of particle production from the effects of quantum statistics and final-state interactions in two-particle correlations. Kaon femtoscopy is an important supplement to that of pions because it allows one to distinguish between different model scenarios working equally well for pions. In particular, we compare the measured three-dimensional kaon radii with a purely hydrodynamical calculation and a model where the hydrodynamic phase is followed by a hadronic rescattering stage. The…

Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe–Xe collisions at sNN=5.44TeV

In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, dNch/dη, and total charged-particle multiplicity, Nchtot, in Xe–Xe collisions at a centre-of-mass energy per nucleon–nucleon pair of sNN=5.44TeV. The measurements are performed as a function of collision centrality over a wide pseudorapidity range of −3.5&lt;η&lt;5. The values of dNch/dη at mid-rapidity and Nchtot for central collisions, normalised to the number of nucleons participating in the collision (Npart) as a function of sNN follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of Npart, and up …

Measurement of dielectron production in central Pb-Pb collisions at √sNN = 2.76 TeV

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. The first measurement of dielectron (e + e −) production in central (0 – 10 %) Pb – Pb collisions at √sNN=2.76TeV at the LHC is presented. The dielectron invariant-mass spectrum is compared to the expected contributions from hadron decays in the invariant-mass range 0 < mee < 3.5 GeV / c2. The ratio of data and the cocktail of hadronic contributions without vacuum ρ0 is measured in the invariant-mass range 0.15 < mee < 0.7 GeV / c2, w…

Elliptic Flow in Pb-Pb Collisions at

We report a precise measurement of the J/ψ elliptic flow in Pb-Pb collisions at sNN=5.02  TeV with the ALICE detector at the LHC. The J/ψ mesons are reconstructed at midrapidity (|y|<0.9) in the dielectron decay channel and at forward rapidity (2.5<y<4.0) in the dimuon channel, both down to zero transverse momentum. At forward rapidity, the elliptic flow v2 of the J/ψ is studied as a function of the transverse momentum and centrality. A positive v2 is observed in the transverse momentum range 2<pT<8  GeV/c in the three centrality classes studied and confirms with higher statistics our earlier results at sNN=2.76  TeV in semicentral collisions. At midrapidity, the J/ψ  v2 is investigated as …

A Note on the Measure of Solvability

An extension of Guo's theorem via k-psi-contractive retraction

Let X be a infinite-dimensional Banach space. We generalize Guo''s Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψ-contractions and condensing mappings, under a condition which depends on the infimum kψ of all k \ge1 for which there exists a k-ψ-contractive retraction of the closed unit ball of the space X onto its boundary.

Examples of proper k-ball contractive retractions in F-normed spaces

Abstract Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r ( X ) of radius r is properly contained in X . The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a ( 1 + e ) -ball contractive retraction of B r ( X ) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X .

Centrality dependence of charged jet production in p–Pb collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s_\mathrm{NN}}$$\end{document}sNN = 5.02 TeV

Measurements of charged jet production as a function of centrality are presented for  p–Pb  collisions recorded at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s_\mathrm {NN}}= 5.02$$\end{document}sNN=5.02 TeV with the ALICE detector. Centrality classes are determined via the energy deposit in neutron calorimeters at zero degree, close to the beam direction, to minimise dynamical biases of the selection. The corresponding number of participants or binary nucleon–nucleon collisions is determined based on…

Measurement of Z 0 -boson production at large rapidities in Pb–Pb collisions at

The production of Z0 bosons at large rapidities in Pb–Pb collisions at √sNN=5.02TeV is reported. Z0 candidates are reconstructed in the dimuon decay channel (Z0→μ+μ−), based on muons selected with pseudo-rapidity −4.0 20GeV/c. The invariant yield and the nuclear modification factor, RAA, are presented as a function of rapidity and collision centrality. The value of RAA for the 0–20% central Pb–Pb collisions is 0.67±0.11(stat.)±0.03(syst.)±0.06(corr. syst.), exhibiting a deviation of 2.6σ from unity. The results are well-described by calculations that include nuclear modifications of the parton distribution functions, while the predictions using vacuum PDFs deviate from data by 2.3σ in the 0…

Measurement of electrons from heavy-flavour hadron decays in p–Pb collisions at sNN=5.02TeV

The production of electrons from heavy-flavour hadron decays was measured as a function of transverse momentum (pT) in minimum-bias p–Pb collisions at √sNN = 5.02 TeV using the ALICE detector at the LHC. The measurement covers the pT interval 0.5 < pT < 12 GeV/c and the rapidity range −1.065 < ycms < 0.135 in the centre-of-mass reference frame. The contribution of electrons from background sources was subtracted using an invariant mass approach. The nuclear modification factor RpPb was calculated by comparing the pT-differential invariant cross section in p–Pb collisions to a pp reference at the same centre-of-mass energy, which was obtained by interpolating measurements at √s = 2.76 TeV an…

Monotonicity and total boundednessin spaces of measurable functions

Abstract We define and study the moduli d(x, 𝓐, D) and i(x, 𝓐,D) related to monotonicity of a given function x of the space L 0(Ω) of real-valued “measurable” functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L 0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness γ(X) of X. Compactness criteria, in special cases, are obtained.

Measurements of mixed harmonic cumulants in Pb–Pb collisions at sNN=5.02 TeV

Correlations between moments of different flow coefficients are measured in Pb–Pb collisions at sNN=5.02 TeV recorded with the ALICE detector. These new measurements are based on multiparticle mixed harmonic cumulants calculated using charged particles in the pseudorapidity region |η|&lt;0.8 with the transverse momentum range 0.2&lt;pT&lt;5.0 GeV/c. The centrality dependence of correlations between two flow coefficients as well as the correlations between three flow coefficients, both in terms of their second moments, are shown. In addition, a collection of mixed harmonic cumulants involving higher moments of v2 and v3 is measured for the first time, where the characteristic signature of ne…

Eigenvectors of k–ψ-contractive wedge operators

Abstract We present new boundary conditions under which the fixed point index of a strict- ψ -contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k – ψ -contractive wedge operators.

On the admissibility of the space L_{0}(A, X) of vector-valued measurable functions

We prove the admissibility of the space L_0(A,X) of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.