Acta Polytechnica. 2016, vol. 56, no. 3http://hdl.handle.net/10467/666162019-08-26T10:48:14Z2019-08-26T10:48:14ZON IMMERSION FORMULAS FOR SOLITON SURFACESGrundland Michel, AlfredLevi , DecioMartina , Luigihttp://hdl.handle.net/10467/814452019-03-14T09:19:27Z2016-01-01T00:00:00ZON IMMERSION FORMULAS FOR SOLITON SURFACES
Grundland Michel, Alfred; Levi , Decio; Martina , Luigi
This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integrable system. After a brief exposition of the theory of soliton surfaces and of the main tool used to study classical and generalized Lie symmetries, we derive the necessary and sufficient conditions under which the immersion formulas associated with these symmetries are linked by gauge transformations. We illustrate the theoretical results by examples involving the sigma model.
2016-01-01T00:00:00ZON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICESLevi , DecioRodriguez A., Miguelhttp://hdl.handle.net/10467/672652017-02-09T11:34:30Z2016-01-01T00:00:00ZON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES
Levi , Decio; Rodriguez A., Miguel
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 is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.
2016-01-01T00:00:00ZTWODIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMSSzajewska , MarzenaTereszkiewicz , Agnieszkahttp://hdl.handle.net/10467/672642017-02-09T11:34:27Z2016-01-01T00:00:00ZTWODIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS
Szajewska , Marzena; Tereszkiewicz , Agnieszka
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 Neumann boundary value problems on F, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of F a Dirichlet condition is fulfilled and on the other Neumann’s works.
2016-01-01T00:00:00ZCOVARIANT INTEGRAL QUANTIZATIONS AND THEIR APPLICATIONS TO QUANTUM COSMOLOGYGazeau , Jean-Pierrehttp://hdl.handle.net/10467/672632017-02-09T11:34:20Z2016-01-01T00:00:00ZCOVARIANT INTEGRAL QUANTIZATIONS AND THEIR APPLICATIONS TO QUANTUM COSMOLOGY
Gazeau , Jean-Pierre
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 labeled by points of the measure space. We especially focus on group representation and probabilistic aspects of these constructions. Simple phase space examples illustrate the procedure: plane (Weyl-Heisenberg symmetry), half-plane (affine symmetry). Interesting applications to quantum cosmology (“smooth bouncing”) for Friedmann-Robertson-Walker metric are presented and those for Bianchi I and IX models are mentioned.
2016-01-01T00:00:00Z