This paper contains a computational analysis and comparison of various representations of a general rigid body spatial screw displacement. Point transformations and line transformations are treated separately. In the context of point transformations, only a brief summary of the known techniques (i.e., homogeneous transforms and quaternion/vector pairs) and their computational behavior is given....

A novel dual-band/dual-mode compact hybrid coupler which acts as a dual-band branch-line at the lower band and rat-race higher is presented in this paper. One of most interesting features proposed structure that outputs each mode operation are on same side. This unique design implemented using artificial transmission lines (ATLs) based open split ring resonators (OSRR). The low-cost miniaturize...

Several common dual quaternion functions, such as the power function, magnitude 2-norm and kth largest eigenvalue of a Hermitian matrix, are standard i.e., parts their function values depend upon only variables. Furthermore, sum, product, minimum, maximum, composite functions two logarithm exponential unit still functions. On other hand, optimization problem, where objective constraint numbers ...

Surprisingly complex tasks can be solved using a behaviour-based, reactive control system, i.e., a system that operates without an explicit internal representation of the environment and the own body. Nevertheless, application of internal representations has gained interest in recent years because such internal representations can be used to solve problems of perception and motor control (senso...

Vertices of the 4-dimensional semi-regular polytope, snub 24-cell and its symmetry group W (D4) : C3 of order 576 are represented in terms of quaternions with unit norm. It follows from the icosian representation of E8 root system. A simple method is employed to construct the E8 root system in terms of icosians which decomposes into two copies of the quaternionic root system of the Coxeter grou...

According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient...

The relationship between finite discrete Zak transform and finite Gabor expansion are well discussed in this paper. In this paper, we present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other is frequencysplit Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between fini...

Quaternions are well suited to describe and combine rotations in the usual 3D euclidian space. Therefore, an increasing interest has been shown especially by engineers for symbolically computing with quaternions. To give the ability to perform manipulations on symbolic expressions involving quaternions, we designed Quaterman, a Maple package and Quaternica, a Mathematica package. We present the...