On Some Mutual Positions of Hyperplanes in a Finite-Dimensional Affine Space

Affine Registration with Feature Space Mutual Information

This paper introduces two important issues of image registration. At first we want to recall the very general definition of mutual information that allows the choice of various feature spaces to perform image registration. Second we discuss the problem of finding the global maximum in an arbitrary feature space. We used a very general parallel, distributed memory, genetic optimization which tur...

FINITE AUTOMORPHISMS OF AFFINE n-SPACE

It is still an open question whether or not there exist polynomial automorphisms of finite order of complex affine n-space which cannot be linearized, i.e., which are not conjugate to linear automorphisms. The second author gave the first examples of non-linearizable actions of positive dimensional groups, and Masuda and Petrie did the same for finite groups. These examples were all obtained fr...

On Some Relationships Among the Association Schemes of Finite Orthogonal Groups Acting on Hyperplanes

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R and determ...

On the number of regions in an m - dimensional space cut by n hyperplanes

In this note we provide a uniform approach for the number of bounded regions cut by n hyperplanes in general position in Rm and the number of regions cut by n great circles in general position in Sm.