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...

It is shown (1) that Lanczos’s quaternionic formulation of Dirac’s equation does not lead to a solution of the problems that plague the standard spin 3/2 theory based on the Rarita-Schwinger equation, but (2) that the fourcomponent solutions to the quaternionic generalization of Dirac’s equation proposed by Lanczos in 1929 may provide a consistent theory for spin 3/2 particles, although at the ...

A 7-manifold with G2 holonomy can be constructed as a R 3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S and CP or its non-compact analogs. This 4-d Einstein space has four isometries and the fixed point set of a generic Killing vector is discussed. ...

We present real, complex, and quaternionic versions of a simple ran-domized polynomial time algorithm to approximate the permanent of a non-negative matrix and, more generally, the mixed discriminant of positive semideenite matrices. The algorithm provides an unbiased estimator, which, with high probability, approximates the true value within a factor of O(c n), where n is the size of the matri...

The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...

This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given pro...

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.

A surface is represented as a quotient of two quaternionic holomorphic sections. Utilizing these quotients, we explain a correspondence between superconformal surfaces and complex holomorphic null curves.