We study three dimensional parametric agile design of gears and related software platforms in terms of: parameterization, modularization, and the software being easy to use, expand and maintain. We base our study on SolidWorks platform, aiming to generate 3-D solid models of gears automatically in terms of: i) inputting parameters to improve the modeling speed, ii) build up foundations for stru...

In this paper, firstly the ruled surface drawn by Darboux vector is expressed as a quaternion. Then, spatial quaternionic definition of striction curve given and integral invariants are calculated. Finally, which corresponds to dual derived with help quaternions obtained.

Some recent work on spaces of algebraic cycles is surveyed. The main focus is on spaces of real and quaternionic cycles and their relation to equivariant EilenbergMacLane spaces.

We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a power series P n∈N qnan in its domain of convergence, which is a ball B(0, R) centered at 0. At each p ∈ B(0, R), f admits expansions in terms of appropriately defined regular power series centered at p, P n∈N (q−p)bn. The expansion holds in a ball Σ(p,R− |p|) defined with r...

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...

Quaternionic polynomials are generated by quaternionic variables and the quaternionic product. This paper proposes the generating ideal of quaternionic polynomials in tensor algebra, finds the Gröbner base of the ideal in the case of pure imaginary quaternionic variables, and describes the normal forms of such quaternionic polynomials explicitly.

It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite dimensional subspaces V of C(B) may not have a solutions in C(B). The corresponding standard short and elegant proof does not apply to complex valued functions over B ⊂ C. Nevertheless, in this sit...