A degree for nonacyclic multiple-valued transformations

Fixed Points of Multiple-valued Transformations

A multiple-valued transformation T from a space X to a space Y is a function assigning to each point x o f X a nonempty closed subset T(x) of F. The graph of T comprises those points (x, y) in the topological product X Y for which y belongs to T(x). All spaces to be considered shall be compact metric and all transformations T shall be upper semi-continuous, meaning that their graphs are closed,...

A Fixed Point Theorem for Continuous Multi-valued Transformations

A Multiple-Valued Logical Semantics for Prolog

Abs t rac t . The coincidence of the declarative and procedural interpretations of logic programs does not apply to Prolog programs, due to the depth-first left-to-right evaluation strategy of Prolog interpreters. We propose a new semantics for Prolog programs based on a new fourvalued logic. The semantics is based on a new concept of completion analogous to Clark's and it enjoys the nice prope...

Learning Transformations with Complex-Valued Neurocomputing

The ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations has been applied to the estimation of optical flows and the generation of fractal images. The complex-valued neural network has the adaptability and the generalization ability as inherent nature. This is the most different point between the ability of the 1-n-1 complex-valued neural network to learn 2D aff...

Degree Elevation for Single-valued Curves in Polar Coordinates

A new class of single-valued curves in polar coordinates obtained by a transformation of a subset of rational B ezier curves into Cartesian coordinates has recently been presented in (SS anchez-Reyes, 1990), and independently considered by P.de Casteljau, who called these curves focal B ezier. These curves are trigonometric polynomials that can be represented by a basis similar to the Bernstein...