### Regular Series

#### Entanglement in the Mixed-three-spin $XXX$ Heisenberg Model with the Next-nearest-neighbour Interaction

abstract

In this paper, we investigate thermal pairwise quantum correlation for any pair of spins of a mixed-three-spin $XXX$ Heisenberg system (with spins connected together with the nearest-neighbour (NN) and that of the next-nearest-neighbour (NNN) coupling constants $J_1$ and $J_2$) by means of concurrence and quantum discord, as functions of temperature $T$, magnetic field $B$ and the coupling constants $J_2$ and $J_1$. Some comparisons between these measures of entanglement are done for next-nearest-neighbour spins. We also express some magnetic properties and discuss the behaviour of the system in some special critical points. Some interesting and novel discussions are done to introduce some entanglement witnesses.

#### Multifractal Flexibly Detrended Fluctuation Analysis

abstract

Multifractal time series analysis is an approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation Analysis (MFDFA). However, it has a drawback. One of its core elements is detrending of the series. In the classical MFDFA, a trend is estimated by fitting a polynomial of degree $m$, where $m=$ const. We propose that the degree $m$ of a polynomial was not constant ($m\neq$ const) and its selection was ruled by an established criterion. Taking into account the above amendment, we examine the multifractal spectra both for artificial and real-world mono- and the multifractal time series. Unlike the classical MFDFA method, obtained singularity spectra almost perfectly reflect the theoretical results, and for real time series, we observe a significant shift at the right-hand side of the spectrum.

#### Rare Semileptonic Decay of $\chi _{c1}(1p)$ Meson in QCD

abstract

The rare semileptonic $\chi _{c1}(1p)\rightarrow D_{s}^{+}e\bar {\nu }$ decay is analyzed by using the three-point QCD sum rules. Taking into account the two-gluon condensate contributions, the transition form factors related to this decay are calculated and are used to determine the total decay width and branching fraction. Our findings may be approved by future experiments.

#### Geometry and Off-shell Nilpotency for $\mathcal {N}=1$ Supersymmetric Yang–Mills Theory

abstract

We show that for $\mathcal {N}=1$ supersymmetric Yang–Mills theory, it is possible to build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST superspace formalism. This is based on the introduction of the basic fields of the quantized theory together with an auxiliary real field via the lowest components of the superfield components of a superYang–Mills connection. Here, the associated supercurvature is constrained by horizontality conditions as in ordinary Yang–Mills theory. We also show how the off-shell BRST-invariant quantum action can be constructed starting from a gauge-fixed superaction.

#### Dynamical Analysis of a New 3D Chaotic System with Coexisting Attractors

abstract

In this paper, a new 3D chaotic system with five nonlinearities is introduced. The basic behaviors of the system are investigated. The dynamic evolution of the system is analyzed by bifurcation diagram, Lyapunov exponents, phase diagram. It is shown that the system generates chaos via Hopf bifurcation and period-doubling bifurcation with the parameters change. The coexisting attractors including point, periodic, chaotic attractors is presented. It is found that the system is abound in coexisting double homologous attractors with respect to different initial values.

all authors

J. Chwastowski, A. Cyz, Ł. Fulek, R. Kycia, B. Pawlik, R. Sikora, J. Turnau

#### Feasibility Studies of Exclusive Diffractive Bremsstrahlung Measurement at RHIC Energies

abstract

Feasibility studies of an observation of the exclusive diffractive bremsstrahlung at RHIC at $\sqrt {s} = 200$ GeV and $\sqrt {s} = 500$ GeV are reported. A simplified approach to the photon and the scattered proton energy reconstruction is used. Influence of possible backgrounds is discussed.

#### Statistical Model of the Early Stage of Nucleus–Nucleus Collisions with Exact Strangeness Conservation

abstract

The Statistical Model of the Early Stage, SMES, describes a transition between confined and deconfined phases of strongly interacting matter created in nucleus–nucleus collisions. The model was formulated in the late 1990s for central Pb+Pb collisions at the CERN SPS energies. It predicted several signals of the transition (onset of deconfinement) which were later observed by the NA49 experiment. The grand canonical ensemble was used to calculate entropy and strangeness production. This approximation is valid for reactions with mean multiplicities of particles carrying conserved charges being significantly larger than one. Recent results of NA61/SHINE on hadron production in inelastic $p+p$ interactions suggest that the deconfinement may also take place in these reactions. However, in this case, mean multiplicity of particles with non-zero strange charge is smaller than one. Thus, for the modelling of $p+p$ interactions, the exact strangeness conservation has to be implemented in the SMES. This extension of the SMES is presented in the paper.

#### Strictly Finite Range Forces from the Signum-Gordon Field: Exact Results in two Spatial Dimensions

abstract

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between charges exceeds certain critical value.

#### On the Longitudinal Structure Function in the Dipole Model

abstract

We compare new HERA data for the longitudinal structure function $F_{\rm L}$ with the predictions of different variants of the dipole model. In particular, we show that the ratio $F_{\rm L}/F_2$ is well described by the dipole models and is rather insensitive to the details of the fit. Fits to $F_2$ are performed with the help of geometrical scaling (GS). Using the property of GS, we derive the bounds for $F_{\rm L}/F_2$ both for the different versions of the dipole model and in the general case. Finally, we briefly discuss how the higher Fock components of the photon wave function may affect these bounds.

#### Forward–Backward Multiplicity Correlations in Relativistic Heavy-ion Collisions

abstract

This study presents the investigations on the occurrence of multiplicity correlations in the particle multiplicities in forward and backward hemisphere in the multiparticle states produced in $^{28}$Si nuclei with various targets at two different energies. The forward–forward and forward–backward dispersions are looked into. The variation of the correlation strength as a function of the pseudorapidity range is investigated and its dependence on target mass as well as the incident energy is studied. In order to estimate the contribution of non-statistical fluctuations, we use the deviation of the value of effective cluster multiplicity from unity as the benchmark.

#### Effects of a Pulsatile Flow and an Endoscope on the Peristaltic Transport of a Newtonian Fluid

abstract

This article analytically investigates the effect of pulsatile flow on the peristaltic transport of a Newtonian fluid between two coaxial cylinders. The inner tube is rigid and uniform and the outer tube has a sinusoidal wave traveling down its wall. This transport is studied under low Reynolds number and long wavelength approximations. The governing equations are developed up to the second order in the Womersley number. We first analyzed the effects of the Womersley, the amplitude ratio and the radius ratio on the pressure rise and on the frictional forces. The instantaneous mechanical efficiency of pumping phenomenon has been graphically presented and the influence of physical parameters on this efficiency has been studied.

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