Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel equalization and beamforming. With most recent developments in quaternion-valued signal processing, in this work, we fill the gap to solve the p...

Expander graphs are graphs in which the neighbors of any given “not too large” set of vertices X form a large set relative to the size of X—rumors tend to spread very fast. Among those, the Ramanujan graphs are extremal in their expansion properties. To be precise, the eigenvalues of the adjacency matrix have an extremal property that guarantees good expansion properties. Expanders, and hence R...

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quater...

The problem of integrating rotations and angular velocity from a known timeand space-dependent curvature is met in the dynamic analysis of non-linear spatial beams, if the numerical formulation is based on curvature, as in [1]. To avoid singularities and make the formulation more convenient, rotational quaternions q̂ are used for the parametrization of rotations. The relation between the curvatu...

Let X be the Shimura curve corresponding to the quaternion algebra over ramified only at 3 and 13. B. Jordan showed that X ( √ −13) is a counterexample to the Hasse principle. Using an equation of X found by A. Kurihara, it is shown here, by elementary means, that X has no ( √ −13)-rational divisor classes of odd degree. A corollary of this is the fact that this counterexample is explained by t...

Impedance control is a well-established framework to manage the interaction of the end effector of a robot manipulator with the environment. For the execution of six-degree-offreedom (DOF) tasks, both the end-effector position and orientation must be handled. The operational space control schemes typically utilize minimal representations of end-effector orientation; however, such representation...

Scene Background Initialization (SBI) is one of the challenging problems in computer vision. Dynamic mode decomposition (DMD) a recently proposed method to robustly decompose video sequence into background model and corresponding foreground part. However, this needs convert color image grayscale for processing, which leads neglect coupling information between three channels image. In study, we ...