In this article, we give a general form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized (3PGQs) and study various properties applications. Firstly present definiton, multiplication table algebraic 3PGQs. matrix representation Hamilton operators for derive polar represenation, De Moivre’s Euler’s formulas with representations Additionally, relations betwee...

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in P. Such pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over Q( √ 5).

It is shown that, in the case of Kerr-Newman space-time, the complex electromagnetic strength E + i H and analogous complex intensity of the gravitational field F attr − i 2 F gyr share the common complexified spatial direction.

Symmetries of complexified space-time and algebraic structures (in quantum theory). Abstract In the paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with " complex Poincaré group " ISO(4, C).

We try to understand the relationship between the K(π, 1)-property of the complexified regular orbit space of a finite reflection group and the flat structure on the orbit space via the uniformization equation attached to the flat structure.

This paper proposes a nonlinear adaptive position and attitude tracking controller for satellite proximity operations between a target and a chaser satellite. The controller requires no information about the mass and inertia matrix of the chaser satellite, and takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth’s oblateness, a...

We examine the dynamics of noncommutative instantons instanton number 2 and commutative 3 in 5D super Yang-Mills theory. begin by detailing construction $1/4$-Bogamolyni-Prasad-Somerfeldt solutions, their moduli space, space potential using an explicit parametrization coordinates terms biquaternions. then go on to numerically analyze spaces we have constructed, discussing some numerical issues ...

Finding the mean (average) of n arbitrary 3D rotations or orientations is conceptually challenging both in its algebra and its geometric interpretation. To my knowledge, no solutions have been found for the general case, although a number of approximate solutions have been proposed [3, 4, 5] to accurately and e ciently handle those limiting cases typical of engineering interest. This report pro...