abstract

We show that, given the generalized chaotic sequences \(x_n=\cos [2\pi \theta z^n]\), where \(z\) is a typical real number, any string \(x_s,x_{s+1},x_{s+2},\ldots ,x_{s+r}\) (for any \(r\)) constitutes a set of statistically independent random variables. We will discuss the relevance of this result to dynamical systems, real physical experiments, and new technological devices used in secure communications.

abstract

Topology of exponential and scale-free trees and simple graphs is investigated numerically. The numbers of the nearest neighbors, the next-nearest neighbors, the next-next-nearest neighbors, the 4-th and the 5-th neighbors are calculated. The functional dependence [A.E. Motter, T. Hishikawa, Y.-Ch. Lai, Phys. Rev. E66, 065103(R) (2002)] of the node-to-node distance \(d_{ij}\) on the product of connectivities \(k_ik_j\) has been studied numerically. The results of simulations for exponential networks agree with the existing analytical predictions.

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In this paper we show that the compensation of loss in the linear fractional oscillator by an active device can result in auto-oscillations. Due to the main feature of linear fractional oscillations, namely a finite number of zeros, the limit cycle in such a generator has a short life time depending on the order of fractional derivative. The electronic circuit, leading to such auto-oscillations, is studied as an example, and its differential equation is derived. The active device characteristic is represented in the piecewise-linear approximation. The features of electric elements are discussed.

abstract

Using the basis of Hermite–Fourier functions (i.e. the quantum oscillator eigenstates) and the Sturm theorem, we derive constraints for a function and its Fourier transform to be both real and positive. We propose a constructive method based on the algebra of Hermite polynomials. Applications are extended to the 2-dimensional case (i.e. Fourier–Bessel transforms and the algebra of Laguerre polynomials) and to adding constraints on derivatives, such as monotonicity or convexity.

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We use a new approach to the UV behavior of quantum general relativity, together with some recent results from the phenomenological asymptotic safety analysis of the theory, to discuss the final state of the Hawking radiation for an originally very massive black hole solution of Einstein’s theory. We find that, after the black hole evaporates to the Planck mass size, its horizon is obviated by quantum loop effects, rendering the entire mass of the originally massive black hole accessible to our Universe.

abstract

Neutron stars are discussed as laboratories of physics of strong gravitational fields. The mass of a neutron star is split into matter energy and gravitational field energy contributions. The energy of the gravitational field of neutron stars is calculated with three different approaches which give the same result. It is found that up to one half of the gravitational mass of maximum mass neutron stars is comprised by the gravitational field energy. Results are shown for a number of realistic equations of state of neutron star matter.

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It is a common knowledge that the quasielastic neutrino–neutron and antineutrino–proton cross sections tend to the same constant as (anti)neutrino energy becomes high. In this paper we calculate the exact expression of the limit in terms of the parameters describing quasielastic scattering. We check that even at very high energies only small absolute values of the four-momentum transfer contribute to the cross section, hence the Fermi theory can be applied. The dipole approximation of the form factors allows to perform analytic calculations. Obtained results are neutrino-flavour independent.

abstract

A decay of a heavy hybrid is expected to produce light mesons flying out with speeds comparable to the speed of light and phenomenological models of the decay must respect symmetries of special relativity. We study consequences of this requirement in a class of simple constituent models with spin. Our models respect boost symmetry because they conform to the rules of a boost-invariant renormalization group procedure for effective particles in light-front QCD. But rotational symmetry of the decay amplitude is not guaranteed and the parameters in the model wave functions must take special values in order to obtain the symmetry. When the effective interaction Hamiltonian responsible for a hybrid decay has the same structure as the gluon–quark–antiquark interaction term obtained by solving the renormalization group equations for Hamiltonians in first order perturbation theory, the non-relativistic image of a hybrid as built from a quark and an antiquark and a heavy gluon that typically resides between the quarks, cannot produce rotationally symmetric amplitude. However, there exists an alternative generic picture in the model that does satisfy the requirements of special relativity. Namely, the distance between the quark and antiquark must be much smaller than the distance between the gluon and the pair of quarks, as if a hybrid were similar to a gluonium in which one gluon is replaced by a quark–antiquark pair.

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Due to anisotropic momentum distributions the parton system produced at the early stage of relativistic heavy-ion collisions is unstable with respect to the magnetic plasma modes. The instabilities isotropize the system and thus speed up the process of its equilibration. The whole scenario of the instabilities driven isotropization is reviewed.

abstract

The “square root” of the Dirac operator derived on the superspace is used to construct supersymmetric field equations. In addition to the recently found solution — a vector supermultiplet — it is demonstrated how another supermultiplet follows as solution: a set of spin 3/2 and spin 1 component fields obeying the appropriate equations of motion together with an auxiliary, spin 2 tensor field.

abstract

The contribution of single-pion photoproduction channels to the spin response of the nucleon, i.e. the asymmetry of photoabsorption cross sections with respect to parallel and antiparallel spins of photon and nucleon, is calculated over the region of the \({\mit \Delta }\)(1232)-resonance adopting an effective Lagrangian model for the reaction amplitude. Furthermore, the contribution from separate pion photoproduction channels to the Gerasimov–Drell–Hearn integral is explicitly evaluated by integration up to a photon lab-energy of 550 MeV. In addition, the double polarization \(E\) asymmetry for the individual pion photoproduction channels is predicted. A quite satisfactory agreement with recent experimental data from the GDH Collaboration is obtained.

abstract

A new family of simple, analytic solutions of self-similarly expanding fireballs is found for systems with ellipsoidal symmetry and a direction dependent, generalized Hubble flow. Gaussian, shell like or oscillating density profiles emerge for simple choices of an arbitrary scaling function. New, cylindrically or spherically symmetric as well as approximately one dimensional hydrodynamical solutions are obtained for various special choices of the initial conditions.

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Coincidence probabilities, which yield Renyi entropies, are investigated in a generalized Gaussian model, which includes interparticle correlations.

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The passage of an ultrasonic wave through a liquid medium can produce cavitation. In this paper we describe the experiment made in order to determine the voltage induced in a cavitation zone and we establish two formulae for the calculus of this voltage, when the studied liquid was the water. The main result is the modeling of an electrical signal induced at the boundary of an acoustic cavitation zone, in water, using the ARIMA process.

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The Fokker–Planck equation for deterministic diffusion out of periodic, nonlinear maps is derived and compared with the random walk and Langevin approaches.