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LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION
(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 ...
ITINERARIES INDUCED BY EXCHANGE OF TWO INTERVALS
(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 ...
MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS
(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 ...
NEW CONCEPT OF SOLVABILITY IN QUANTUM MECHANICS
(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 ...
NOTE ON VERMA BASES FOR REPRESENTATIONS OF SIMPLE LIE ALGEBRAS
(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] ...
EXAMPLES OF QUANTUM HOLONOMY WITH TOPOLOGY CHANGES
(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 ...
gln+1 ALGEBRA OF MATRIX DIFFERENTIAL OPERATORS AND MATRIX QUASI-EXACTLY-SOLVABLE PROBLEMS
(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
(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
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)
Foreword
COULOMB SCATTERING IN NON-COMMUTATIVE QUANTUM MECHANICS
(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). ...