Showing papers in "Reports on Mathematical Physics in 2004"

TL;DR: In this paper, the authors studied the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan and found that the linear harmonic oscillator appears as the λ → 0 limit of this oscillator whose energy spectrum and eigenfunctions are compared to the linear ones.

TL;DR: In this article, a geometric setting for the Pontryagin maximum principle in optimal control theory is provided, where the equations for critical trajectories are given in terms of a symplectic equation, and these equations are generalized to the framework of Lie algebroids, giving thus a way to study reduction by symmetry groups of the maximum principle.

TL;DR: In this paper, the theory of singular reduction for implicit Hamiltonian systems admitting a symmetry Lie group was developed, where the reduction is performed at a singular value of the momentum map.

TL;DR: In this article, the controllability of first order semilinear impulsive functional differential inclusions in the case where the right hand side is convex or nonconvex valued is investigated.

TL;DR: In this paper, a condition for the function λ to determine a type of von Neumann algebra generated by the GNS construction associated with the unordered phase of the λ-model is given.

TL;DR: In this article, the vertical parts of the gauge-natural lifts of infinitesimal principal automorphisms are considered as canonical generators of covariant superpotential currents and superpotentials.

TL;DR: In this article, the authors present a new, elementary proof for Wigner's unitary-anti-unitary theorem, which they call unitary anti-Wigner theorem.

TL;DR: This framework allows the number of equations associated with optimal control problems with symmetry to be reduced and the reconstruction of the optimal controls starting from the reduced problem is explored.

TL;DR: In this paper, a direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model.

TL;DR: In this paper, the Green-Naghdi theory of nonlinear thermoelasticity without dissipation is studied and the balance laws on the material manifold are derived and the exact conditions under which they hold are rigorously studied.

TL;DR: In this article, a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups is proposed, which is affinely-invariant.

TL;DR: In this article, the entanglement of formation for a large class of quantum mixed states is explicitly presented, and a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices.

TL;DR: In this paper, the mass gap problem is related to the finite-dimensional spectral problem for a generalized Clifford-valued magnetic Schrodinger operator which represents the DW Hamiltonian operator.

TL;DR: In this paper, discontinuous Sturm-Liouville problems with eigenvalue parameters both in equation and in boundary conditions are investigated and asymptotic approximate formulae for eigenvalues and normalized eigenfunctions are obtained.

TL;DR: It is shown that the covariant coarse-grainings of sharp observables are exactly the covariate fuzzy observables, which are necessary and sufficient for a covariant fuzzy observable to be informationally equivalent to the corresponding sharp observable.

TL;DR: In this paper, the authors define and study the Ingarden spaces, I F n, as Finsler spaces equipped with the Lorentz nonlinear connection and establish the formula dω = F + θ.

TL;DR: In this article, the Marsden-Weinstein reduction procedure for almost symplectic manifolds is implemented and conditions for transformation of non-equivariant momentum maps into equivariant ones by modifying the group action are studied.

TL;DR: In this paper, the authors extend the results of Derezinski-Gerard and Gerard about the self-adjointness, the location of the essential spectrum and the existence of a ground state to a large class of Pauli-Fierz Hamiltonians.

TL;DR: In this article, a method to construct exact solutions of nonlinear partial differential equations (NLPDEs) in a unified way is presented, which is named an improved sine-cosine method.

TL;DR: In this article, it was shown that each element of a Rickart comgroup has a rational spectral resolution and a nonempty closed and bounded (real) spectrum, and that the spectrum has many of the properties of the spectral resolution of a self-adjoint operator on a Hilbert space.

TL;DR: In this paper, it was shown that affine spray induces covariant derivatives in the tangent or pull-back bundles of a manifold M and vice versa, similarly to Weyl's relation.

TL;DR: It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressable.

TL;DR: In this paper, the role of the phase parameter leading to unitarily equivalent operators is discussed, and it is shown that the phase is not redundant (contrary to previous studios) if nonstationary problems are concerned.

TL;DR: In this paper, a tensor product in the category of Hilbert space effect algebras is defined such that the tensor products reflect as much as possible of the physically important properties of the components.

TL;DR: In this paper, the definition of Dirac-Nijenhuis manifolds (DN-manifolds) is given and the properties and relations among them, including their properties and their relations among Poisson-and Nijenhais manifold types.

TL;DR: In this paper, a twisted product of two quantum subgroups SUq(2) and Uq(1) is constructed, and the multiplicative unitary (Kac-Takesaki) operator for this quantum group is given.

TL;DR: In this paper, the three-level atomic system interacting with one mode of the electromagnetic field in a Ξ-configuration is investigated, and effective Hamiltonians for two-photon processes without the rotating wave approximation are obtained by application of the perturbation method of multiple time scales.

TL;DR: In this article, a new context is introduced to give a formal geometric environment for the study of impulsive mechanics of systems with finite number of degrees of freedom, such as tangent bundles for time independent systems and jet-bundles for time dependent ones.

TL;DR: In this article, the properties of a four-level atomic system interacting with one and two modes of the electromagnetic field in a "Ξ" configuration were investigated, and it was shown that the corresponding mathematical models are exactly solvable.

TL;DR: In this paper, a general criterion of invariance of integro-differential equations under Lie symmetry group of point transformations is derived, which is a generalization of the previous form of the criterion to the case of a moving range of integration.