Acta Polytechnica. 2013, vol. 53, no. 5
http://hdl.handle.net/10467/66596
2019-03-21T08:36:57ZFOREWORD: THREE QUARTERS A CENTURY
http://hdl.handle.net/10467/67091
FOREWORD: THREE QUARTERS A CENTURY
Exner , Pavel
Foreword
2013-01-01T00:00:00ZTHE NUMBER OF ORTHOGONAL CONJUGATIONS
http://hdl.handle.net/10467/67090
THE NUMBER OF ORTHOGONAL CONJUGATIONS
Uhlmann , Armin
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 open problem.
2013-01-01T00:00:00Zgln+1 ALGEBRA OF MATRIX DIFFERENTIAL OPERATORS AND MATRIX QUASIEXACTLYSOLVABLE PROBLEMS
http://hdl.handle.net/10467/67089
gln+1 ALGEBRA OF MATRIX DIFFERENTIAL OPERATORS AND MATRIX QUASIEXACTLYSOLVABLE PROBLEMS
Smirnov F., Yuri; Turbiner , Alexander
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 Calogero and Sutherland models are presented.
2013-01-01T00:00:00ZLIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION
http://hdl.handle.net/10467/67088
LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION
Levi , Decio; Winternitz , Pavel
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 schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.
2013-01-01T00:00:00Z