This paper researches properties of a regular function defined on a domain in Clifford analysis. Also, the paper investigates properties of extensions for a regular function with values in DH and the corresponding Cauchy-Riemann system for a regular function of dual quaternionic variables.

Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotational matrices, a need for unambiguous, compact, s...

Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 3 and standard module V . Recently Ito and Terwilliger introduced four direct sum decompositions of V ; we call these the (μ, ν)–split decompositions of V , where μ, ν ∈ {↓, ↑}. In this paper we show that the (↓, ↓)–split decomposition and the (↑, ↑)–split decomposition are dual with respect to the standard Hermitian form on V...

Each of the local isometry groups arising in 3d gravity can be viewed as the group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement, and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for Euclidean signature with positi...

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...

In this work, we propose an approach for extrinsic sensor calibration from per-sensor ego-motion estimates. Our problem formulation is based on dual quaternions, enabling two different online capable solving approaches. We provide a certifiable globally optimal and fast local along with method to verify the globality of approach. Additionally, means integrating previous knowledge, example, comm...

Using dual quaternions, the closure equations of a kinematic loop can be expressed as system multiaffine equations. In this paper, property is leveraged to introduce branch-and-prune method specially tailored for solving such systems The new objectively simpler (in sense that it easier understand and implement) than previous approaches relying on general techniques interval Newton methods or ba...