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    • THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES 

      Autor: Bodner , Mark; Chadzitaskos , Goce; Patera , Jiří; Tereszkiewitz , Agnieszka
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      About 60 years ago, I. Shmushkevich presented a simple ingenious method for computing the relative probabilities of channels involving the same interacting multiplets of particles, without the need to compute the Clebsch-Gordan ...
    • COULOMB SCATTERING IN NONCOMMUTATIVE QUANTUM MECHANICS 

      Autor: Gáliková , Veronika; Prešnajder , Peter
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      Recently we formulated the Coulomb problem in a rotationally invariant NC configuration space specified by NC coordinates xi, i = 1, 2, 3, satisfying commutation relations [xi, xj ] = 2iλεijkxk (λ being our NC parameter). ...
    • RESONANCES ON HEDGEHOG MANIFOLDS 

      Autor: Exner , Pavel; Lipovský , Jiří
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering ...
    • ON RENORMALIZATION OF POISSON–LIE TPLURAL SIGMA MODELS 

      Autor: Hlavatý , Ladislav; Navrátil , Josef; Šnobl , Libor
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      Covariance of the one-loop renormalization group equations with respect to Poisson–Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson–Lie sigma models with ...
    • PROPOSAL OF NEW OPTICAL ELEMENTS 

      Autor: Chadzitaskos , Goce; Tolar , Jiří
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      A overview of our patented proposals of new optical elements is presented. The elements are suitable for laser pulse analysis, telescopy, X-ray microscopy and X-ray telescopy. They are based on the interference properties ...
    • ITINERARIES INDUCED BY EXCHANGE OF TWO INTERVALS 

      Autor: Masáková , Zuzana; Pelantová , Edita
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We focus on the exchange T of two intervals with an irrational slope α. For a general subinterval I of the domain of T, the first return time to I takes three values. We describe the structure of the set of return itineraries ...
    • EXTREMAL VECTORS FOR VERMA TYPE REPRESENTATION OF B2 

      Autor: Burdík , Čestmír; Navrátil , Ondřej
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      Starting from the Verma modules of the algebra B2 we explicitly construct factor representations of the algebra B2 which are connected with the unitary representation of the group SO(3, 2). We find a full set of extremal ...
    • EXAMPLES OF QUANTUM HOLONOMY WITH TOPOLOGY CHANGES 

      Autor: Cheon , Taksu; Tanaka , Atushi; Turek , Ondřej
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We study a family of closed quantum graphs described by one singular vertex of order n = 4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed path in the parameter space that ...
    • LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION 

      Autor: Levi , Decio; Winternitz , Pavel
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference ...
    • NEW CONCEPT OF SOLVABILITY IN QUANTUM MECHANICS 

      Autor: Znojil , Miloslav
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      In quite a few recent quantum models one is allowed to make a given Hamiltonian H self-adjoint only after an ad hoc generalization of Hermitian conjugation, H†→H‡:= Θ −1H†Θ wherethe suitable operator Θ is called Hilbert-space ...
    • MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS 

      Autor: Riečanová , Zdenka; Janda , Jiří
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We show that in any generalized effect algebra (G;⊕, 0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;⊕, 0), called a summability block. If G is lattice ordered, then every summability ...
    • NOTE ON VERMA BASES FOR REPRESENTATIONS OF SIMPLE LIE ALGEBRAS 

      Autor: Pošta , Severin; Havlíček , Miloslav
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      We discuss the construction of the Verma basis of the enveloping algebra and of finite dimensional representations of the Lie algebra An. We give an alternate proof of so-called Verma inequalities to the one given in [1] ...
    • gln+1 ALGEBRA OF MATRIX DIFFERENTIAL OPERATORS AND MATRIX QUASIEXACTLYSOLVABLE PROBLEMS 

      Autor: Smirnov F., Yuri; Turbiner , Alexander
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      The generators of the algebra gln+1 in the form of differential operators of the first order acting on Rn with matrix coefficients are explicitly written. The algebraic Hamiltonians for matrix generalization of 3−body ...
    • THE NUMBER OF ORTHOGONAL CONJUGATIONS 

      Autor: Uhlmann , Armin
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      After a short introduction to anti-linearity, bounds for the number of orthogonal (skew) conjugations are proved. They are saturated if the dimension of the Hilbert space is a power of two. For other dimensions this is an ...
    • FOREWORD: THREE QUARTERS A CENTURY 

      Autor: Exner , Pavel
      (České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
      Foreword