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In the past ** G. Kaniadakis** has collaborated on articles with

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AbstractOptical measurements (UV-visible-NIR) have been performed at room temperature on sputtered a-SiC:H samples after annealing at temperatures, Ta, between 673 and 973 K. The complex dielectric constant in the range of 0.8–6.5 eV and, using the Wemple-Di Domenico model, the dispersion energy, the Penn gap, the valence electron density, the plasmon energy and the Fermi energy were deduced. The energy gap was determined by means of various models. The decrease of energy gap and the increase of the valence electron density on one hand, and the shift of the exponential absorption edge on the other hand, indicate the coupling of the valence and the conduction band states by optical photon as the annealing temperature increases. Moreover, as Ta exceeds 773 K, the polycrystalline phase can be observed to germinate inside the pre-existing amorphous phase.

AbstractContemporary transition description, in the nearest neighbors frame, allows a more complete and rigorous treatment of the kinetics of a system of identical particles obeying an exclusion-inclusion principle than the only individual transition approximation. Within this description, statistical distributions are derived, as stationary states of a generalized non linear Fokker-Planck equation, and collective quantum macroscopic effects for both bosons and fermions can be evidentiated in a more precise form and with a more appropriate meaning than in the indidual transition approximation.

AbstractA space scaling procedure is proposed for the treatment of diffusion problems in large lattices. In conjunction with a previously proposed time scaling procedure, space scaling yields a renormalization group technique, which can reduce by an almost arbitrarily large factor both the computer time and the number of lattice sites for a diffusion problem with or without drift. Several numerical examples demonstrate the efficiency and reliability of the method.

AbstractWe consider a wide class of nonlinear canonical quantum systems described by a one-particle Schrödinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the continuity equation. In this way we are able to obtain a new quantum system obeying a nonlinear Schrödinger equation with a real nonlinearity. As an application of this theory we consider a few already studied Schrödinger equations, such as that containing the nonlinearity introduced by the exclusion-inclusion principle, the Doebner-Goldin equation and other ones.

AbstractWe present a class of nonlinear Schrödinger equations (NLSEs) describing, in the mean field approximation, systems of interacting particles. This class of NLSEs is obtained generalizing expediently the approach proposed in [G. K., Phys. Rev. A 55, 941 (1997)], where a classical system obeying to an exclusion-inclusion principle is quantized using the Nelson stochastic quantization. The new class of NLSEs is obtained starting from the most general nonlinear classical kinetics compatible with a constant diffusion coefficient D = h/2m. Finally, in the case of s-stationary states, we propose a transformation which linearizes the NLSEs here proposed.

AbstractWe propose a new nonrelativistic abelian Maxwell-Chern-Simons model describing a collectively interacting particle system obeying a generalized Exclusion-Inclusion Principle. Starting from the Lagrangian of the system, in the frame of the canonical formalism, we derive the equations of motion for matter and gauge fields. Within this model we write and study the Ehrenfest relations. Finally, we show that the energy of the system is limited at the lower boundary, independent of the value of the parameter which quantifies the action of the Exclusion-Inclusion Principle.

AbstractBy solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.

AbstractThis paper proposes the κ-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement–such as the Lorenz curve and the Gini coefficient–are given. A method for parameter estimation is also discussed. The model is shown to fit extremely well the data on personal income distribution in Australia and in the United States.

AbstractA justified modification of the real part of the complex non-linearity of a Schrödinger equation, recently proposed G. Kaniadakis, Phys. Rev. A 55 (1997) 941], allows us to obtain a new canonical quantum system obeying an exclusion–inclusion principle. The soliton solutions of this new effective Schrödinger equation are obtained in an implicit form.

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