Water Sources Diagram and Its Applications

Near Pole Polar Diagram of Points and its Duality with Applications

In this paper we propose a new approach to plane partitioning with similar features to those of Polar Diagram, but we assume that the pole is close to the sites. The result is a new tessellation of the plane in regions called Near Pole Polar Diagram NPPD. Here we define the (NPPD) of points, the dual and the Contracted dual of it, present an optimal algorithms to draw them and discuss the appli...

Crystal Voronoi diagram and its applications

This paper studies the multiplicatively weighted crystal-growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. The analytic equation describing the boundary curve is given for a simple case. For the general case, an approximation algorithm is proposed....

Voronoi Diagram in the Laguerre Geometry and its Applications

We extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line, and show that there is an O(n log n) algorithm for this extended case. The Voronoi diagram in the Laguerre geometry may be applied to solving effectiv...

Diagram: the Synoptics and Their Sources

Benford Distribution and its Applications

‎This papers considers the Benford distribution as one the interesting rules of probability theory‎. ‎This rule shows that‎, ‎despite of usual underestanding about the uniform distribution of digites‎ ‎for lieing on different positions in numbers‎, ‎digits are distributed according to an non uniform distributions for numbers araising from many natural phonemena‎. ‎Benford distribution proposes ...