Partial discretization and preservation relations

Preservation of Adiabatic Invariants under Symplectic Discretization

Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example, in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small fluctuations that scale with the order of the method. In this paper, we discuss a qualitative fe...

Affine Spheres: Discretization via Duality Relations

Preservation of piecewise-linear Lyapunov function under Padé discretization

In this paper we show that certain piecewiselinear Lyapunov functions are preserved for LTI systems under Padé approximations. In particular, we present a simple method to find a piecewise-linear Lyapunov function that is so preserved under the Padé discretization of any order and sampling time. This result may be of interest in the discretisation of switched linear systems for both simulation ...

Preservation of Intuitionistic Fuzzy Preference Relations

In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

Reasoning about Domain Semantics over Relations, Bags, Partial Relations, and Partial Bags

Quality database schemata must capture both the structure and semantics of the domain of interest. Classes of data dependencies have been studied extensively to model domain semantics. Traditionally, the theory of data dependencies has been limited to relations. In practice, duplicate and partial information are permitted to occur in database instances. These features are supported to make data...