Classifying quadratic maps from plane to plane

Fold Maps from the Sphere to the Plane

Classifying lattice walks restricted to the quarter plane

This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras’ walks; two new non-holonomic classes; and enumer...

Integer quadratic programming in the plane

Bounded Quadratic Systems in the Plane*

This paper contains a study of those two-dimensional autonomous systems with quadratic polynomial right-hand sides which have all of their trajectories bounded for t > 0. Such systems will be referred to as bounded quadratic systems. It follows from the PoincarbBendixson Theorem that any such system will have a rest point in the plane and by translating the origin to that rest point it will hav...

Plane 1 Plane 2 Plane 1 Plane

This paper introduces a Relative Mapping Algorithm. This algorithm presents a new way of looking at the SLAM problem that does not use Probability, Iterative Closest Point, or Scan Matching techniques. A map of landmarks is generated by using the average relative location difference between landmarks. This means the algorithm does not use any known, estimated or predicted movement or position d...