The articles [13], [4], [5], [2], [14], [3], [8], [6], [15], [9], [16], [10], [11], [12], [7], and [1] provide the notation and terminology for this paper. One can prove the following proposition (1) For all non-empty sets A, B, C and for every function f from A into B such that for every element x of A holds f(x) ∈ C holds f is a function from A into C. In the sequel A will be a non-empty set ...

We present an algorithmic procedure to further reduce (Poincar e) Normal Forms; we give both general results and methods, and a concrete application.

The aim of this paper is to demonstrate a speciic application of Computer Algebra to bifurcation theory with symmetry. The classiication of diierent bifurcation phenomena in case of several parameters is automated, based on a classiication of Grr obner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with...

Normal forms have been introduced as approximating relations for fuzzy relations. Moreover, they can be viewed as a formalization of a collection of fuzzy IF-THEN rules. Therefore, investigation of approximating abilities of normal forms together with determination of an appropriate inference engine contributes to building of fuzzy systems.

In this chapter we present normal forms for the design of multimedia database schemes with reduced manipulation anomalies. To this aim we first discuss how to describe the semantics of multimedia attributes based upon the concept of generalized icons, already used in the modeling of multimedia languages. Then, we introduce new extended dependencies involving different types of multimedia data. ...

Normal form procedure This is the stepwise ‘simplification’ by changes of coordinates, of the Taylor series at an equilibrium point, or of similar series at periodic or quasi-periodic solutions. Preservation of structure The normal form procedure is set up in such a way that all coordinate changes preserve a certain appropriate structure. This applies to the class of Hamiltonian or volume prese...

This brief note compares a few ways of deriving pre-orders over sets of objects from strict partial orders over properties of those objects— so-called priority graphs that have recently been used by logicians as a rich explicit model of preference merge, belief revision, norm change, and other aspects of agency. Our note establishes equivalence results between three popular formats for priority...