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    • ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES 

      Autor: Levi , Decio; Rodriguez A., Miguel
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem ...
    • ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS 

      Autor: Gubbiotti , Giorgio; Levi , Decio; Scimiterna , Christian
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this ...
    • COVARIANT INTEGRAL QUANTIZATIONS AND THEIR APPLICATIONS TO QUANTUM COSMOLOGY 

      Autor: Gazeau , Jean-Pierre
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators ...
    • LAPLACE EQUATIONS CONFORMAL SUPERINTEGRABILITY AND BÔCHER CONTRACTIONS 

      Autor: Kalnins G., Ernest; Miller, Jr , Willard; Subag , Eyal
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often ``hidden''.The symmetry generators of 2nd order superintegrable systems in 2 dimensions close ...
    • ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS 

      Autor: Háková , Lenka; Hrivnák , Jiří; Motlochová , Lenka
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems. The diagram containing the relations ...
    • A SUPERINTEGRABLE MODEL WITH REFLECTIONS ON S^3 AND THE RANK TWO BANNAIITO ALGEBRA 

      Autor: De Bie , Hendrik; Genest Xavier, Vincent; Lemay , Jean-Michel; Vinet , Luc
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed ...
    • THE AHARONOVBOHM HAMILTONIAN WITH TWO VORTICES REVISITED 

      Autor: Košťáková , Petra; Stovicek , Pavel
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      We consider an invariant quantum Hamiltonian H = −ΔLB + V in the L2 space based on a Riemannian manifold ˜M with a discrete symmetry group Γ. To any unitary representation Λ of Γ one can relate another operator on M = ˜M ...
    • IS PT SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY 

      Autor: Znojil , Miloslav
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014)) that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory”) is ...
    • THREEVARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS 

      Autor: Bezubik , Agata; Pošta , Severin
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing ...
    • TWODIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS 

      Autor: Szajewska , Marzena; Tereszkiewicz , Agnieszka
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2016)
      Boundary value problems are considered on a simplex F in the real Euclidean space R2. The recent discovery of new families of special functions, orthogonal on F, makes it possible to consider not only the Dirichlet or ...