Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat r...

The evolute of a conic in the pseudo-Euclidean plane is locus centers all its osculating circles. It’s curve order six and class four general case. In this paper we discuss compute evolutes different types conics. We will highlight those cases that have no analogy Euclidean plane.

The increasing amount of roaming Internet users in combination with the evolution of IP-based applications has created a strong demand for wide-area, broadband access to a number of IP multimedia services. Wireless LANs can complement the next-generation cellular networks, by offering a cost-efficient, wireless broadband data solution for hot spot areas. By combining the wide coverage of next-g...

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain N = 2 supergravity theories, where dimensional reduction induces a mapping between special real, Kähler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the Kähler and quaternionic manifolds in homogeneous holomorphic f...

The infinite-dimensional Clifford algebra has a maze of inequivalent irreducible unitary representations. Here we determine their type -real, complex or quaternionic. Some, related to the Fermi-Fock representations, do not admit any real or quaternionic structures. But there are many on L of the circle that do and which seem to have analytic meaning. Table of contents.

In this paper, novel non-involute cylindrical gears are designed based on a curved path of contact. Firstly, parabolic curve is predesigned as the contact gears. Then, tooth profiles calculated using differential geometry and spatial meshing theory. Secondly, three-dimensional models established according to machining simulation. Thirdly, simulation model (including misalignment error longitudi...

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.

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...