Acta Polytechnica  

P. Ambrož

Let ß > 1 be a cubic Pisot unit. We study forms of Thurston tilings arising from the classical ß-numeration system and from the (-ß)-numeration system for both the Ito-Sadahiro and balanced definition of the (-ß)-transformation.

P. Amore,F. M. Fernández

We study a harmonic molecule confined to a one-dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate e... see more

S. Duplij,S. Sinel’shchikov

To give the complete list of Uq (sl2)-actions of the quantum plane, we first obtain the structure of quantum plane automorphisms. Then we introduce some special symbolic matrices to classify the series of actions using the weights. There are uncountably m... see more

M. Havlícek,E. Pelantová,J. Tolar

This paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is applied to finite-dimensional representations of sl(n,C) in relation to its Z2-gradings. For r... see more

M. Havlícek,S. Pošta

(so3) is demonstrated. The approach presented here is successful in other cases of quantum algebras and superalgebras.

V. Jakubský

We briefly review the relation between the Aharonov-Bohm effect and the dynamical realization of anyons. We show how the particular symmetries of the Aharonov-Bohm model give rise to the (nonlinear) supersymmetry of the two-body system of identical anyons... see more

M. Kalina,J. Paseka,Z. Riecanová

Special types of effect algebras E called sharply dominating and S-dominating were introduced by S. Gudder in [7, 8]. We prove statements about connections between sharp orthocompleteness, sharp dominancy and completeness of E. Namely we prove that in eve... see more

D. Kochan

Path integral formulation of quantum mechanics (and also other equivalent formulations) depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to a p... see more

T. Mine

We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac d measures supported on a discrete set G in M. We give a complete characterization of the self-adj... see more

I. Rotter

In the framework of non-Hermitian quantum physics, the relation between exceptional points,dynamical phase transitions and the counter intuitive behavior of quantum systems at high level density is considered. The theoretical results obtained for open qua... see more

B. Shapiro

This paper is a brief survey of the research conducted by the author and his collaborators in the field of root asymptotics of (mostly polynomial) eigenfunctions of linear univariate differential operators with polynomial coefficients.

M. Znojil

Certain complex-contour (a.k.a. quantum-toboggan) generalizations of Schroedinger’s bound-state problem are reviewed and studied in detail. Our key message is that the practical numerical solution of these atypical eigenvalue problems may perceivably be f... see more