Abstract: The six degrees-of-freedom (DoFs) nonsingular pose tracking is the prerequisite for the smooth task executions in many robot-assisted medical scenarios, such as laparoscopic surgery and ...

ABSTRACT: In this paper, from the spacetime algebra associated with the Minkowski space ℝ 3,1 by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion ...

ABSTRACT: Originally, Maxwell attempted to express his electromagnetic theory using four-dimensional mathematics of quaternions. Maxwell’s equations were later re-written in a three-dimensional real ...

Abstract: In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion ...

After faculty protests and a debate over racial equity, the state’s public universities reconsider whether high school students can skip a foundational course. By Amy Harmon Since 2020, California has ...

Ghost Dirac’s fermions are a manifestation of virtual particles. One fermion is the particle whose companion is the antiparticle. An ensemble of these fermions coupled in pairs represents the ...

Gravitomagnetic equations result from applying quaternionic differential operators to the energy–momentum tensor. These equations are similar to the Maxwell’s EM equations. Both sets of the equations ...

We prove a higher dimensional generalization of Gross and Zagier’s theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of ...