We investigate the vacuum polarization, \(\langle \phi ^{2}\rangle ,\) of the quantized massive scalar field with a general curvature coupling parameter in the spatially-flat \(N\)-dimensional Friedman–Robertson–Walker spacetime with \(4\leq N \leq 12\). The vacuum polarization is constructed using both adiabatic and Schwinger–DeWitt approaches and the full final results up to \(N=7\) are explicitly demonstrated. The behavior of \(\langle \phi ^{2}\rangle \) for \(4\leq N \leq 12\) is examined in the exponentially expanding universe, in the power-law and inflationary power-law models. In the case of exponential expansion, \(\langle \phi ^{2}\rangle \) is constant and for a given mass it depends solely on the Hubble constant and the curvature coupling parameter. In the power-law models its behavior is more complicated and, generally, decays in time as \(t^{-n},\) where \(n/2\) is the integer part of \(N/2\). The \(2+1\)-dimensional case is also briefly analyzed. The relevance of the present results to the stress-energy tensor is examined.

We derive the energy levels for oscillator model defined on the twisted \(N\)-enlarged Newton–Hooke space-time, i.e. , we find time-dependent eigenvalues and corresponding time-dependent eigenstates. We also demonstrate that for a particular choice of deformation parameters of phase space, the above spectrum can be identified with the time-dependent Landau one.

We present a stochastic model where random walker can change its position according to two competing motions: Gaussian motion or Lévy flights and at each step, the type of motion is chosen randomly. We assume that contribution from all processes to the entire process is determined by the probabilities of appearances to each of them. For large times and spatial distance, we derive fractional differential equation describing the evolution of the probability density. This asymptotic form is determined by parameters describing stochastic motion: probabilities of occurrence of the Gaussian motion and Lévy flights, and two diffusion constants. We also show that for the initial density in the form of the Dirac delta function, this model has the analytic solution given in the integral form. For other forms of initial densities, we present results of numerical solutions for various model parameters.

An analysis of twist composition of Balitsky–Kovchegov (BK) amplitude is performed in the double logarithmic limit. In this limit, the BK evolution of color dipole–proton scattering is equivalent to BFKL evolution which follows from vanishing of the Bartels vertex in the collinear limit. We perform twist decomposition of the BFKL/BK amplitude for proton structure functions and find compact analytic expressions that provide accurate approximations for higher twist amplitudes. The BFKL/BK higher twist amplitudes are much smaller than those following from eikonal saturation models.

Exact solution of a coupled spin-electron linear chain composed of localized Ising spins and mobile electrons is found with the use of a transfer-matrix method. The ground-state phase diagram consists of three phases with different number of mobile electrons per unit cell, one of which is paramagnetic, one is ferromagnetic and one is antiferromagnetic. Thermal variations of specific heat with up to four distinct peaks are observed, while temperature dependences of isothermal electron compressibility reveal a round maximum at low temperatures when the investigated system is driven close to the ground-state boundary between the ferromagnetic and antiferromagnetic phase.

Indices of heart rate variability are calculated twice: firstly from signals with unperturbed normal \(RR\)-intervals, and subsequently from the same signals edited according to either real patterns of disturbances or random patterns of perturbations. Four methods of editing are applied: (I) deletion of abnormal \(RR\)-intervals, (II) replacement of abnormal \(RR\)-intervals by the median, (III) replacement of abnormal \(RR\)-intervals by a random value from the surrounding \(RR\)-intervals, (IV) entering the values that result from the statistics of similar patterns. The fractality indices, such as \(\alpha _1\) and \(\alpha _2\) from detrended fluctuation analysis (DFA), and a ratio of \(RR\)-intervals greater than 50 ms, pNN50, are found to be the most sensitive to editing, independently of the method of editing and the organization of the disturbance pattern.

Intelligent agent systems are relatively new approach to modelling social phenomena. In particular, such systems are descriptions and simplified representation of human interactions occurring in real world. In the paper, a model of intelligent agents system, in which the agents interact with environment and change their opinions as a result of mutual contacts, is presented. A network of inter-agents contacts was constructed to investigate the process of self-organization in the system resulting from agents motion and their opinion formation. The relations between the properties of this network, properties of environment and opinion formation rules were discussed. It is worth noting that in contrast to other papers, we examined two general threads studied so far separately: opinion dynamics of autonomous agents, and the relation between agents and resources distribution in the environment.