Inscribed rectangle coincidences

We prove an integral formula for continuous paths of rectangles inscribed in a piecewise smooth loop. We use this integral formula to prove the inequality M(γ) ≥ Δ(γ)/2 – 1, where M(γ) denotes the total multiplicity of rectangle coincidences, i.e. pairs, triples, etc. of isometric rectangles inscribed in γ, and Δ(γ) denotes the number of stable diameters of γ, i.e. critical points of the distance function on γ.

Angular correlations in pA collisions from CGC: multiplicity and mean transverse momentum dependence of $$v_2$$

Within the dense-dilute Color Glass Condensate approach, and using the Golec–Biernat–Wuesthoff model for the dipole scattering amplitude, we calculate $$v_2^2$$ v 2 2 as well as the correlations between $$v_2^2$$ v 2 2 and both the total multiplicity and the mean transverse momentum of produced particles. We find that the correlations are generally very small consistent with the observations. We note an interesting sharp change in the value of $$v^2_2$$ v 2 2 as well as of its correlations as a function of the width of the transverse momentum bin. This crossover is associated with the change from Bose enhancement dominance of the correlation for narrow bin to HBT dominated correlations for larger bin width.

CENTER PROBLEM FOR CUBIC DIFFERENTIAL SYSTEMS WITH THE LINE AT INFINITY AND AN AFFINE REAL INVARIANT STRAIGHT LINE OF TOTAL MULTIPLICITY FOUR

In this article, we show that a non-degenerate monodromic critical point of differential systems with the line at infinity and an affine real invariant straight line of total multiplicity four is a center type if and only if the first four Lyapunov quantities vanish.

Collective phenomena in hadron and nuclear interactions at high multiplicity

Multiparticle production is described in the language of quarks and gluons. In the experiment the real hadrons are registered. For transfer from quarks and gluons to observed hadrons, various phenomenological models are used. In order to describe the high multiplicity region, we have developed a gluon dominance model. It represents a convolution of two stages. First stage is described by QCD. For second one (hadronisation), the phenomenological model is used. The description of topological cross sections in p $ \bar p $ collisions within of our model testifies that in hadron collisions the mechanism of hadronisation is being replaced by the recombination one. At that point, gluons play an active role in the multiparticle production process, and valence quarks are passive. They stay in the leading particles, and only the gluon splitting is responsible for the region of high multiplicity. The model with inclusion of intermediate quark charged topologies describes topological cross sections in annihilation. We observe the significant growth of a scaled variance of number of neutral pions with increasing of the total multiplicity at U-70 accelerator at IHEP (Protvino). The following experiment with 3.5 A GeV deuteron, lithium and carbon beams of the Nuclotron (JINR, Dubna) falling at a carbon target is carried out at the NIS-GIBS setup. The noticeable excess yield of soft photons(pT < 50 MeV/c) is observed. The existing models based on Monte Carlo simulation and theoretical estimations predict a lower yield. Our Collaboration plans to study excess of soft photon yield and other phenomena at the SPD (Spin Physics Detector) setup at JINR, Dubna with polarised beams of proton and light nuclei up to 25 GeV.