Showing papers in "Reports on Mathematical Physics in 1998"

TL;DR: In this paper, the authors studied the structure of classical field theory in n dimensions within the covariant polymomentum Hamiltonian formulation of De Donder-Weyl (DW) and proposed a bi-vertical (n + 1)-form, called polysymplectic, which gives rise to the invariantly defined map between horizontal forms playing the role of dynamical variables and the vertical multivectors generalizing Hamiltonian vector fields.

TL;DR: In this article, a geometric setting for the Hamiltonian description of mechanical systems with a nonholonomic constraint is proposed, which may be used for constraints of general type (nonlinear in the velocities, and such that the constraint forces may not obey Chetaev's rule).

TL;DR: In this article, the authors investigate various aspects of the interplay of an affine connection with a distribution and derive conservation laws in the case when the original connection is the Levi-Civita connection associated with Riemannian metric.

TL;DR: In this paper, the authors further develop the theory of nonholonomic Poisson reduction, and use this reduction procedure to organize non-holonomic dynamics into a reconstruction equation and the reduced Lagrange d'Alembert equations in the Hamiltonian form.

TL;DR: In this article, it was shown that the observed exponential stability of such systems can follow solely from the nonholonomic nature of intermittent contact and not from dissipation, and that discrete nonholonomy can contribute to exponential stability.

TL;DR: In this paper, a geometric reduction procedure for Lagrangian systems subjected to nonlinear nonholonomic constraints in the presence of symmetries is presented, based on a geometrical method which enables one to deduce the constrained dynamics from the unconstrained one by projection.

TL;DR: In this paper, it is shown how Dirac structures can be reduced to Dirac structure on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system.

TL;DR: A necessary and sufficient condition for a function to be a constant of motion of a Lagrangian system with nonlinear nonholonomic constraints is derived in the framework of the Hamiltonian formulation as discussed by the authors.

TL;DR: The Prytz planimeter is a simple example of a system governed by a nonholonomic constraint as discussed by the authors, which is unique among planimeters in that it measures something more subtle than area, combining the area, centroid and other moments of the region being measured.

TL;DR: In this article, simple explicit transformations which turn the associated indicatrix metric tensors into a canonical constant-curvature form are shown. But these transformations can further be extended to operate over the tangent space.

TL;DR: In this paper, some nonlinear parabolic-elliptic systems were proposed to model the evolution of the density of particles interacting with themselves, and coupled to a temperature field.

TL;DR: In this article, it was shown that the integral map of Routh's sphere has monodromy when the sphere becomes gyroscopically unstable, using the non-Hamiltonian non-monodromy theorem.

TL;DR: In this article, the authors examined the nonholonomic bracket with a view to doing singular non-holonomic reduction, which explains not only the seeming paradox of asymptotic stability in Hamiltonian systems but yields a geometrically faithful framework for studying singularity in the tippe top.

TL;DR: It is shown that the standard random variables are in one-to-one correspondence to the extreme points of the convex set of all fuzzy random variables with the same outcome space.

TL;DR: In this paper, a model of particles equipped with generalized statistics is developed, and commutation relations and corresponding consistency conditions are given in terms of quantum Weyl algebras.

TL;DR: In this paper, it was shown that the moment operators of any of the phase space observables associated with the number states are the powers of the lowering operator, and that all moment operators are integer valued polynomials of the number operator.

TL;DR: In this article, a tensor product of morphisms, bimorphisms, and tensor products of effect algebras is computed and a class of mappings on a Hilbert space called quadratic state-forms is presented.

TL;DR: In this article, the problem of computing reduced equations for mechanical systems with nonholonomic constraints, Lie group symmetries, and dissipative forces has been addressed for both the unconstrained and constrained cases.

TL;DR: In this article, a constructive approach to differential calculus on quantum principal bundles is presented, starting from given graded (differential) ∗-algebras representing horizontal forms on the quantum base space, together with a family of antiderivations acting on horizontal forms, playing the role of covariant derivatives of certain special connections.

TL;DR: In this article, the spectral basis of the propulsion operator is used to describe the surface deformations of a sphere inside a viscous fluid, and the authors compare two notions of efficiency for locomotion processes modelled by linear variational problems with nonholonomic constraints.

TL;DR: In this article, the motion of a nonlinear nonholonomically constrained system which after reduction realizes a nonrelativistic classical particle with spin was described, and the motion was shown to be nonlinear and nonholonomic.

TL;DR: In this article, a relativistic description of rotations that restores the full covariance of electromagnetism was proposed, and the distortion of the scattering pattern generated by rotation disappears in this case for a perfectly conducting cylinder.

TL;DR: In this paper, the Marsden-Ratiu geometrical reduction for Poisson manifolds is extended to Nambu-Poisson and generalized Poisson manifold and several applications are given.

TL;DR: In this paper, F -rotations which leave Finslerian metric functions invariant are derived systematically and the invariant metric tensors and fundamental frame fields are also derived.

TL;DR: In this article, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite dimensional Hamiltonian system and a quasi-local Hamiltonian which possesses direct physical interpretation being equal to the total energy of the composed system (field + particle).

TL;DR: In this paper, a model for the periodic system of the Aharonov-Bohm rings is constructed by means of operator extension theory, where the uniform component of the field has a rational flux through an elementary cell of the Bravais lattice of the system, in an explicit form.

TL;DR: In this article, the k-mode fluctuations of observables in a quasi-local C ∗ -algebra A and a state ω are studied, and shown to be normal under mild cluster conditions.

TL;DR: In this paper, the method of additional generating conditions for obtaining new exact solutions of nonlinear evolution equations (see [16]) was further developed, and some new non-Lie ansatze and exact solutions were obtained for two classes of reaction-diffusion equations with the power and exponential nonlinearities, which describe real processes in physics, chemistry, and biology.

TL;DR: In this paper, it was proven that three related measures of stability in quantum mechanics (for autonomous, periodic and quasiperiodic Hamiltonians) are, in fact, equivalent.

TL;DR: In this paper, the authors consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables and show that random dilution can change the limiting eigenvalue distribution of such matrices.