A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Актуальні питання реалізації іпотечних зобов'язань в нотаріальному процесі

Стаття присвячена теоретичному дослідженню важливості використання існуючих механізмів превентивної юстиції та дієвості правозахисної функції нотаріату. Доведено, що нотаріус як гарант превентивності правовідносин реалізує свої правозахисні функції не лише на стадії реалізації іпотечних зобовязань, шляхом вчинення виконавчого напису на борговому документі, а і на стадії узгодження та викладення всіх істотних умов договору. Ключові слова: нотаріат; правозахисна функція нотаріату; виконання зобовязань; превентивна юстиція.Статья посвящена теоретическому исследованию необходимости использования существующих механизмов превентивной юстиции и действенности правозащитной функции нотариата. Доказывается, что нотариус как гарант превентивности правоотношений реализует свои правозащитные функции не только на стадии реализации ипотечных обязательств, в связи с совершением исполнительной надписи на долговом документе, а и на стадии согласования и изложения всех существенных условий договора. Ключевые слова: нотариат; правозащитная функция нотариату; исполнение обязательств; превентивная юстиция.This article is dedicated into theoretical research of importance in using special mechanism of prevention justitia and acting law defender functions of notoriety. It is argued that notaries as a guaranty of prevention law relation realizes his law defender functions not only on the stage of realization ipothek obligations, making performance inscription on the duty document, but on the stage of consenting and stating all existence conditions of contract. Key words: notoriety, law defender function of notaries, making obligations, prevention justitia

Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions

At sufficiently high temperature and energy density, nuclear matter undergoes a transition to a phase in which quarks and gluons are not confined: the quark-gluon plasma (QGP)(1). Such an exotic state of strongly interacting quantum chromodynamics matter is produced in the laboratory in heavy nuclei high-energy collisions, where an enhanced production of strange hadrons is observed(2-6). Strangeness enhancement, originally proposed as a signature of QGP formation in nuclear collisions(7), is more pronounced for multi-strange baryons. Several effects typical of heavy-ion phenomenology have been observed in high-multiplicity proton-proton (pp) collisions(8,9), but the enhanced production of multi-strange particles has not been reported so far. Here we present the first observation of strangeness enhancement in high-multiplicity proton-proton collisions. We find that the integrated yields of strange and multi-strange particles, relative to pions, increases significantly with the event charged-particle multiplicity. The measurements are in remarkable agreement with the p-Pb collision results(10,11), indicating that the phenomenon is related to the final system created in the collision. In high-multiplicity events strangeness production reaches values similar to those observed in Pb-Pb collisions, where a QGP is formed.Peer reviewe

Longitudinal asymmetry and its effect on pseudorapidity distributions in Pb-Pb collisions at root s(NN)=2.76 TeV

First results on the longitudinal asymmetry and its effect on the pseudorapidity distributions in Pb-Pb collisions at root s(NN) = 2.76 TeV at the Large Hadron Collider are obtained with the ALICE detector. The longitudinal asymmetry arises because of an unequal number of participating nucleons from the two colliding nuclei, and is estimated for each event by measuring the energy in the forward neutron-Zero-Degree-Calorimeters (ZNs). The effect of the longitudinal asymmetry is measured on the pseudorapidity distributions of charged particles in the regions vertical bar eta vertical bar < 0.9, 2.8 < eta < 5.1 and -3.7 < eta < -1.7 by taking the ratio of the pseudorapidity distributions from events corresponding to different regions of asymmetry. The coefficients of a polynomial fit to the ratio characterise the effect of the asymmetry. A Monte Carlo simulation using a Glauber model for the colliding nuclei is tuned to reproduce the spectrum in the ZNs and provides a relation between the measurable longitudinal asymmetry and the shift in the rapidity (y(0)) of the participant zone formed by the unequal number of participating nucleons. The dependence of the coefficient of the linear term in the polynomial expansion, c(1), on the mean value of y(0) is investigated.Peer reviewe

Production of deuterons, tritons, He-3 nuclei, and their antinuclei in pp collisions at root s=0.9, 2.76, and 7 TeV

Invariant differential yields of deuterons and antideuterons in pp collisions at root s = 0.9, 2.76 and 7 TeV and the yields of tritons, He-3 nuclei, and their antinuclei at root s = 7 TeV have been measured with the ALICE detector at the CERN Large Hadron Collider. The measurements cover a wide transverse momentum (p(T)) range in the rapidity interval vertical bar y vertical bar <0.5, extending both the energy and the pT reach of previous measurements up to 3 GeV/c for A = 2 and 6 GeV/c for A = 3. The coalescence parameters of (anti) deuterons and 3 He nuclei exhibit an increasing trend with pT and are found to be compatible with measurements in pA collisions at low p(T) and lower energies. The integrated yields decrease by a factor of about 1000 for each increase of the mass number with one (anti) nucleon. Furthermore, the deuteron-to-proton ratio is reported as a function of the average charged particle multiplicity at different center-of-mass energies.Peer reviewe

D-Meson Azimuthal Anisotropy in Midcentral Pb-Pb Collisions root S-NN=5.02 TeV

The azimuthal anisotropy coefficient v(2) of prompt D-0, D+, D*+, and D-s(+) mesons was measured in midcentral (30%-50% centrality class) Pb-Pb collisions at a center-of-mass energy per nucleon pair root s(NN)=5.02 TeV, with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at midrapidity, |y| < 0.8, in the transverse momentum interval 1 < p(T) < 24 GeV/c. The measured D-meson v(2) has similar values as that of charged pions. The D-s(+) v(2), measured for the first time, is found to be compatible with that of nonstrange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters.Peer reviewe

Linear and non-linear flow mode in Pb-Pb collisions at root sNN=2.76 TeV

The second and the third order anisotropic flow, V-2 and V-3, are mostly determined by the corresponding initial spatial anisotropy coefficients, epsilon(2) and epsilon(3), in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn(n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V-n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range |eta| <0.8 and the transverse momentum range 0.2 <p(T)<5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system. (C) 2017 The Author(s). Published by Elsevier B.V.Peer reviewe