The equivalence between neutral particles under rotation and charged in a magnetic field relates phenomena as diverse spinning atomic nuclei, weather patterns, the quantum Hall effect. In their descriptions, translations along different directions do not commute, implying Heisenberg uncertainty relation spatial coordinates. Here, we exploit ability to squeeze non-commuting variables dynamically...

Over the past several decades there has been steady progress towards the goal of polynomial-time approximation schemes (PTAS) for fundamental geometric combinatorial optimization problems. A foremost example is the geometric hitting set problem: given a set P of points and a set D of geometric objects, compute the minimum-sized subset of P that hits all objects in D. For the case where D is a s...

We introduce infinitary propositional theories over a set and their models which are subsets of the set, and define a generalized geometric theory as an infinitary propositional theory of a special form. The main result is that the class of models of a generalized geometric theory is set-generated. Here a class X of subsets of a set is set-generated if there exists a subset G of X such that for...

Geometric algebra covers many mathematical areas such as vector algebra, complex numbers, Pluecker coordinates, quaternions. It is geometrically intuitive and has a lot of potential for optimization and parallelization. In this paper, we develop an approach for the specialized machine instruction set GAPP based on our table-based compilation approach for geometric algebra computing. GAPP can be...

This article developed a new method to described the set of stabilizing PID control. The is based on D-parameterization with natural description set. It was found that stability crossing surface ruled completely determined by curve known as discriminant. discriminant divided into sectors at cusps. Corresponding sectors, positive and negative patches. A systematic study conducted identify region...