Designing dependable process-oriented software : a CSP-based approach

This thesis advocates dependability as a crucial aspect of software quality. Process orientation, as it is defined in this thesis, concentrates on the notion of a process as a basic building component of a dataflow-centred software architecture. The dependability approach in the proposed variant of process orientation builds on a few specific strengths of the particular dataflowcentred architecture which is based on the principles of the CSP process algebra

Noether symmetries and integrability in time-dependent Hamiltonian mechanics

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative) integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.Comment: 18 pages, 2 figures, to appear in Theoretical and Applied Mechanic

Heisenberg model in pseudo-Euclidean spaces

We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system) on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove that the Heisenberg model on a light--like cone leads to a new example of integrable discrete contact system.Comment: 6 page

On the principle of stationary isoeneretic action

We present several variants of the Maupertuis principle, both on the exact and the non exact symplectic manifolds.Comment: 19 pages, 2 figure