An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

This paper discusses a trainable system to extract features for image segmentation based on non-linear mapping of local features. Supervised training methods are presented, for artificial neural diabolo networks, which produce a mapping comparable to Fisher’s linear discriminant mapping. This mapping can be used to decrease dimensionality whilst preserving class separability. It is shown that t...

Two groups of pattern-recognition algorithms for hybrid optical-digital computer processing are theoretically and experimentally compared. The first group is based on linear mapping, while the second group is based on feature extraction and eigenvector analysis. We study the relations among various linear-mapping-based algorithms by formulating a more general unified pseudoinverse algorithm. We...