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[en] The rarely mentioned fact that a pure boost in general distorts the axes of the boosted frame is shown to influence significantly the Thomas precession effect as observed in the laboratory frame. As a result the Thomas precession appears to be accompanied by a ‘wobbling’ motion of the axes of precessing rest frame connected with a moving particle. A simple method to get an exact solution for the development of the orientation of the frame axes in the case of uniform rotation of the particle is given. This is equivalent to finding the orientation of the spin vector used in the BMT theory. The discrepancy known from the literature in describing the spin, as performing a uniform rotation or as revealing in the same situation some additional oscillatory behaviour, is explained by pointing out two conceptually different approaches, ‘hybrid’ and fully consistent, in presenting the Thomas precession. (paper)
[en] We proposed the discrete Euler top in 2000. In that paper, exact solutions and conserved quantities are described. However, a Lax pair of our proposed discrete Euler top is not contained. Moreover, the Lax pair is still unknown. In this paper, from a generalized eigenvalue problem, we obtain the Lax pair of the discrete Euler top. (paper)
[en] We find a new class of exact solutions in the Einstein-Maxwell theory by employing the Ernst magnetization process to the Kerr-Newman-Taub-NUT spacetimes. We study the solutions and find that they are regular everywhere. We also find the quasilocal conserved quantities for the spacetimes, the corresponding Smarr formula and the first law of thermodynamics.
[en] In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev-Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae
[en] A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansaetze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are obtained. The relation of the solutions obtained with the development of spatially inhomogeneous structures is discussed
[en] In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
[en] In this paper we derive convergence and convergence rates results for a new parameter selection criterion for regularization methods based on spectral theory when applied to linear ill-posed problems Tx = y. We prove convergence and suboptimal rates under a qualitative condition on the decay of the noise with respect to the spectral family of TT*. Moreover, optimal rates are obtained if the exact solution satisfies a decay condition with respect to the spectral family of T*T