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By resorting to the nonlinearization approach, a Bargmann constraint associated with a discrete \(3\times 3\) matrix eigenvalue problem is considered. The lattice soliton hierarchy and the bi-Hamiltonian structures are obtained. A new symplectic map of the Bargmann type is obtained by nonlinearization of the discrete eigenvalue problem and its adjoint one. With the help of the generating function, we arrive at the involutive system of conserved integrals of the symplectic map, which is further proved to be completely integrable.

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We consider brane cosmology when the 4D Ricci scalar term is added to the 5D Einstein–Hilbert action and discuss the role that the addition of this term has on the brane-bulk system. The induced brane dynamics is shown to be the usual Einstein dynamics coupled to a modified energy-momentum tensor which is well defined once the 5D Einstein equations are solved in the bulk. The 5D Einstein equations valid everywhere in the bulk, but not in the brane, are projected on the brane. Then making use for the embedding of the brane in the bulk of the Israel junction conditions, modified by a source term coming from the addition of the intrinsic curvature scalar in the bulk action, it is possible to obtain the effective 4D Einstein equations on the brane consistent with the bulk geometry.

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A controlled teleportation scheme of a two-qubit state in general form is proposed. The sender performs four-qubit jointly projective measurement and tells the measurement outcome to the receiver. The receiver performs the unitary transformations on his qubits to obtain the original state under the cooperation of the controller.

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This paper investigated chaos control of four-dimensional autonomous van der Pol Mathieu (vdPM) system that describes dust-charge fluctuation in dusty plasma. A recursive backstepping scheme was employed to design a single control input that effectively controlled the undesirable unstable behaviour of the vdPM system. Both theoretical analysis and numerical simulations were presented to illustrate the effectiveness of the proposed control scheme.

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In this paper we discuss decomposition principle for \(\alpha \)-stable Lévy processes. We investigate asymptotic properties of components and stochastic integrals driven by such processes providing an important class of anomalous diffusions. We consider two case studies with integrands being fractional Brownian motion and gamma process.

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The gravitational field exterior respectively interior to an axially symmetric, metrically stationary, isolated spinning source made of perfect fluid is examined within the quasi-metric framework. (A metrically stationary system is defined as a system which is stationary except for the direct effects of the global cosmic expansion on the space-time geometry.) Field equations are set up and solved approximately for the exterior part. To lowest order in small quantities, the gravitomagnetic part of the found metric family corresponds with the Kerr metric in the metric approximation. On the other hand, the gravitoelectric part of the found metric family includes a tidal term characterized by the free quadrupole-moment parameter \(J_2\) describing the effect of source deformation due to the rotation. This term has no counterpart in the Kerr metric. Finally, the geodetic effect for a gyroscope in orbit is calculated. There is a correction term, unfortunately barely too small to be detectable by Gravity Probe B, to the standard expression.

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The Renyi entropies, \(H_l\), of Hawking radiation contained in a thin shell surrounding the black hole are evaluated. When the width of the shell is adjusted to the energy content corresponding to the mass defect, the Bekenstein–Hawking formula for the Shannon \((S=H_1)\) entropy of a black hole is reproduced. This result does not depend on the distance of the shell from the horizon. The Renyi entropies of higher order, however, are sensitive to it.

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We assume that the cold dark matter consists of spin-1/2 and spin-0 particles described by a bispinor field \(\psi \) and a scalar field \(\varphi \), sterile from all Standard Model (SM) charges (in contrast, neutralinos, supersymmetric candidates for cold dark matter, are not sterile from weak SM charges). We propose, however, that such a sterile world can contact with our SM world not only through gravity but also through a portal provided by photons coupled to sterile particles by means of two very weak effective interactions \(-(~f\)/\(M^{~2})\varphi F^{~\mu \nu }\varphi F_{\mu \nu }\) and \(-(~f'\)/\(M^{~2}) \bar {\psi }\sigma ^{\mu \nu }\psi \varphi F_{\mu \nu }\), where \(M\) is a very large mass scale and \(f\) and \(f'\) are dimensionless coupling constants. Thus, in our picture, the electromagnetic field \(F_{\mu \nu }\) — as the only SM field — participates in both worlds, providing a nongravitational link between them (other than the popular supersymmetric weak interaction, active in the case of neutralinos). In consequence, there appears a tiny quasi-magnetic correction to the conventional electromagnetic current (described in Appendix A).

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We propose a framework of SU(5) supersymmetric grand unified theory with the minimal particle contents, which does not contain dimension five proton decay operators. The suitable fermion mass hierarchy can be reproduced by higher dimensional operators of an adjoint Higgs field which breaks SU(5) gauge symmetry.

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Predictions for the spin dependent structure function \(g_1\) of the nucleon are presented. We use an unified approach incorporating the LO DGLAP evolution and the resummation of double logarithmic terms \(\ln ^2(x)\). We show, that the singular input parametrisation as \(x\rightarrow 0\) can be a substitute of the \(\ln ^2(x)\) resummation. An impact of the ‘more running’ coupling is discussed. We determine the contribution to the Bjorken sum rule solving the evolution equation for the truncated moment of \(g_1^{\rm NS}\). A comparison with the re-analysed HERMES and COMPASS data is given.

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Using the generalized zeta-function method we discuss the influence of a uniform magnetic field on the Casimir energy of a fermionic field submitted to a general boundary condition which interpolates continuously periodic and antiperiodic ones. After computing the relevant fermionic determinant we show that the Casimir effect can be enhanced by the external magnetic field, in agreement to the known results established in the literature. We also compute the corresponding Casimir pressure and present the result graphically by sketching its behavior as a function of the magnetic field and the parameter \(\theta \) which defines the boundary condition. This analytical result is a new one in the known literature.

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Revised analysis of \({\mit \Sigma }\) beam asymmetry for \(\eta \) photoproduction off the free proton from GRAAL is presented. New analysis reveals a narrow structure near \(W\sim 1.685\) GeV. We describe this structure by the contribution of a narrow resonance with quantum numbers \(P_{11}\), or \(P_{13}\), or \(D_{13}\). Being considered together with the recent observations of a bump-like structure at \(W\sim 1.68\) GeV in the quasi-free \(\eta \) photoproduction off the neutron, this result provides an evidence for a narrow (\({\mit \Gamma } \leq 25\) MeV) \(N^{~*}(1685)\) resonance. Properties of this possible new nucleon state, namely the mass, the narrow width, and the much stronger photocoupling to the neutron, are similar to those predicted for the non-strange member of anti-decuplet of exotic baryons.

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Multiplicity distributions of projectile fragments emitted in gold-emulsion (Au–Em) collisions at 10.7\(A\) GeV are reported. The projectile lithium and heavier fragments show an exponential multiplicity distribution. The projectile helium and hydrogen fragments show a single peak and a two-peak multiplicity distributions, respectively. These distributions are studied using a two-phase model.

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The ratios of particle densities in lead–lead and proton–lead collisions to particle density in proton–proton collision in the central rapidity region at the LHC energy are predicted on the basis of wounded quark–diquark model.

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The algorithm rotating the real spherical harmonics is presented. The convenient and ready to use formulae for \(\ell = 0, 1, 2, 3\) are listed. The rotation in \(\mathbb {R}^3\) space is determined by the rotation axis and the rotation angle; the Euler angles are not used. The proposed algorithm consists of three steps. (i) Express the real spherical harmonics as the linear combination of canonical polynomials. (ii) Rotate the canonical polynomials. (iii) Express the rotated canonical polynomials as the linear combination of real spherical harmonics. Since the three step procedure can be treated as a superposition of rotations, the searched rotation matrix for real spherical harmonics is a product of three matrices. The explicit formulae of matrix elements are given for \(\ell = 0, 1, 2, 3\), what corresponds to \(s, p, d, f\) atomic orbitals.

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The aim of this paper is to present a new method of classification of the stellar spectra. The parameters characterizing the spectra are moments of intensity distributions. Statistical Theory of Spectra is used as a tool for the classification of the stellar spectra. The method of using distribution moments has been already proposed by the present authors as new molecular descriptors in the theory of molecular similarity. In this paper the method is implemented in astrophysics. Moments of intensity distributions have different values for every spectral type. We present diagrams based on the knowledge of the moments in which all types of stars can be recognized. Distribution moments obtained from the experimental spectra can be helpful to recognize easily the spectral type.

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The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of the model are reduced to the form which allows a direct comparison between them and the equations of the Einsteinian classical theory of gravity. It is shown that quantized scalar field has a form of a condensate which behaves as an anti-gravitating medium. The theory predicts an accelerating expansion of the universe even if the vacuum energy density vanishes. An anti-gravitating effect of a condensate has a purely quantum nature. It is shown that the universe with the parameters close to the Planck ones can go through the period of exponential expansion. The conditions under which in semi-classical approximation the universe looks effectively like spatially flat with negative deceleration parameter are determined. The reduction to the standard model of classical cosmology is discussed.