We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...

A planar spiral called Generalized Log Aesthetic Curve segment (GLAC) has been proposed using the curve synthesis process with two types of formulation; ρ-shift and κ-shift. Both methods were carried out by extending the formulation of Generalized Cornu Spiral (GCS) in a similar manner to the Log Aesthetic Curve (LAC). The family of GLAC comprises of planar curves of high quality such as GCS, L...

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

Abstract. We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component ...

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CH, n ≥ 3. For the quaternionic hyperbolic spaces HH, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificatio...

This paper focuses on the geometric theory of scroll compressor, which includes the determination of the discharge angle, the calculation of the volume in different compression stages, the axial gas force under the condition that the number of scroll turns equals an arbitrary real number. NOMENCLATURE . (J :expanding angle of the involute (rad) a :initial angle of the involute (rad) 6 : orbitin...

A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space HPn. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces M = G/H by viewing HPn ≃ U(n + 1, H)/U(1, H)× U(n, H) ≃ Sp(n + 1)/Sp(1)× Sp(...

The purpose of this research was to evaluate the nonlinear dynamic response of rigid and semi-rigid steel frames under Far-Fault Earthquake Records. Accordingly, the fragility curve of the moment frames with rigid and semi-rigid connections was determined. Considering the analytical knowledge of structures in the past, the analysis and design of steel frames based on the assumptions of rigid or...