Guest lecture at an international conference with published abstract
B.04 Guest lecture
COBISS.SI-ID: 16299097Invited series of lectures (6 hours) at the International Summer School, Université Joseph Fourier, Grenoble, Francija
B.04 Guest lecture
COBISS.SI-ID: 16556121In this paper we construct a new Lax pair for the Klein-Gordon equation. The structure algebra of this Lax pair is the algebra ▫$\mathcal{TA}_2$▫ of upper triangular Toeplitz block matrices with ▫$\mathfrak{su}(2)$▫ blocks. For the suitable choice of the values of the spectral parameter, the integrals of motion, obtained from the holonomy of the spatial part of the Lax pair, have simple expressions in terms of the Fourier data. We compare these integrals to the corresponding integrals of the sine-Gordon system.
B.03 Paper at an international scientific conference
COBISS.SI-ID: 16406105Polynomial geometric interpolation by parametric curves has become one of the standard techniques for interpolation of geometric data. An obvious generalization leads to rational geometric interpolation schemes, which are a much less investigated research topic. The aim of this paper is to present a general framework for Hermite geometric interpolation by rational Bézier spatial curves. In particular, cubic $G^2$ and quartic $G^3$ interpolations are analyzed in detail. Systems of nonlinear equations are derived in a simplified form, and the existence of admissible solutions is studied. For the cubic case, geometric conditions implying solvability of the nonlinear system are also stated. The asymptotic analysis is done in both cases, and optimal approximation orders are proved. Numerical examples are given, which confirm the theoretical results.
B.03 Paper at an international scientific conference
COBISS.SI-ID: 16330329A textbook in Slovenian language; introductory complex analysis.
D.10 Educational activities
COBISS.SI-ID: 263239936