This qualitative, action research methodology study aims at the construction of a teaching unit for development learning processes, analyzing trajectories students around geometric proportionality in topics related to similarity, homothecy, and Thales’ theorem. The didactic was designed under principles phases van Hiele’s (1986) model, mathematical visualization, use GeoGebra software. Among re...

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, n-ary operations for all n greater than or equal to 0, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation show...

Geometric probing considers problems of determining a geometric structure or some aspect of that structure from the results of a mathematical or physical measuring device, a probe. A variety of problems from robotics, medical instrumentation, mathematical optimization, integral and computational geometry, graph theory and other areas fit into this paradigm. This paper surveys the field of geome...

Geometric algebra has been proved to be a powerful mathematical language for robot vision. We give an overview of some research results in two different areas of robot vision. These are signal theory in the multidimensional case and knowledge based neural computing. In both areas a considerable extension of the modeling has been achieved by applying geometric algebra.

Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to optimize classifier probabilities, thereby increasing classification accuracy. We unify major quantification approaches under a constrained multi-variate re...

• Symmetry analysis of differential equations: classical and nonclassical symmetries, potential symmetries, group–invariant solutions, variational symmetries and conservation laws • Applications of symmetry analysis theory to mathematical models arising in mathematical physics, mathematical biology, image processing, engineering, financial mathematics and other research fields • Geometric appro...

We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and i...

Geometric algebra is an universal mathematical language which provides very comprehensive techniques for analyzing the complex geometric situations occurring in artiicial Perception Action Cycle systems. In the geometric algebra framework such a system is both easier to analyze and to control in real time computations. This paper describes the application of rotors and motors for tasks involvin...