In this paper, we give a beginners guide to the practicality of using dual-quaternions to represent the rotations and translations in character-based hierarchies. Quaternions have proven themselves in many fields of science and computing as providing an unambiguous, un-cumbersome, computationally efficient method of representing rotational information. We hope after reading this paper the reade...

We define motion polynomials as polynomials with coefficients in the dual quaternions and study their factorizations. The motion polynomials correspond to motions in 3D space, and factoring into linear factors means to compose the motion into translations and rotations. This allows to realize the motion by a linkage with revolute or prismatic joints. This is joint work with G. Hegedüs (Univ. Ob...

1. A. F. Horadam. "Basic Properties of a Certain Generalized Sequence of Numbers." The Fibonacci Quarterly 3 (1965):161-75. 2. A. F. Horadam. "Complex Fibonacci Numbers and Fibonacci Quaternions." Amer. Math. Monthly 70 (1963):289-91. 3. A. L. Iakin. "Generalized Quaternions with Quaternion Components." The Fibonacci Quarterly 15 (1977):35Q-52. 4. A. L. Iakin. "Generalized Quaternions of Higher...

A quaternionic representation of the genetic code, previously reported by the authors (BioSystems 141 (10-19), 2016), is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation associates with each nucleotide base a prime integer quaternion of norm 7 and involves a function that assigns to each codon, represented by three of these quaternions, ...

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance 1/n. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension n goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on mo...

In recent years, real-valued neural networks have demonstrated promising, and often striking, results across a broad range of domains. This has driven surge applications utilizing high-dimensional datasets. While many techniques exist to alleviate issues high-dimensionality, they all induce cost in terms network size or computational runtime. work examines the use quaternions, form hypercomplex...

The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting Delsarte–Goethals–Seidel upper bound are obtained.

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...