In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with ⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution .

The collection of all quaternions is denoted byH and is called the real quaternionic algebra. This algebra was first introduced by Hamilton in 1843 (see [5, 6]), and is often called the Hamilton quaternionic algebra. It is well known thatH is an associative division algebra over R. For any a= a0 + a1i+ a2 j + a3k ∈H, the conjugate of a = a0 + a1i + a2 j + a3k is defined to be a = a0 − a1i− a2 j...

In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an underlying noncommutative dynamics. In quaternionic quantum mechanics, the Dirac transition amplitudes 〈ψ|φ〉 are quaternion valued, that is, they have the for...

The paper investigates the properties of ambiguity functions of 2-D analytic, quaternionic and monogenic signals. In the introduction the notions of the above signals and their Wigner distributions and ambiguity functions are recalled. The properties of the ambiguity functions are investigated using two kinds of test signals: A band-pass test signal in the form of a sum of two harmonic signals ...

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same special geometry that is known from nonlinear sigma models in N = 2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of extra and h...

We present in this paper the advantages of using the model of Euclidean paths for the geometrical analysis of a discrete curve. The Euclidean paths are a semi-continuous representation of a discrete path providing a good approximation of the underlying real curve. We describe the use of this model to obtain accurate estimations of lenght, tangent orientation and curvature.

In this thesis we build the parametric mathematical model of machine tool and solid models of traction gears using in subway locomotive by analyzing the machining process of involute gears and meshing principle of involute gears. The optimization design is done through deduce the relations between basic parameters of gear and loading capacity of transmission. On the base of analyzing optimizati...

The equivalence relations of strict equivalence and congruence of real and complex matrix pencils with symmetries are compared, depending on whether the congruence matrices are real, complex, or quaternionic. The obtained results are applied to comparison of congruences of matrices, over the reals, the complexes, and the quaternions.

This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips [4]. Due to Phillips' fundamental theorems helical involute gears for parallel axes (Fig. 2) serve also as tooth flanks for a uniform transmission between skew axes, and the transmission ratio is even independent of the relative position of the axes.