Ordered affine local ternary rings and ordered affine Klingenberg planes

Subspace operations in affine Klingenberg spaces

In two previous papers we introduced the notion of an Affine Klingenberg space A and presented a geometric description of its free subspaces. Presently, we consider the operations of join, intersection and parallelism on the free subspaces of A. As in the case of ordinary affine spaces, we obtain the Parallel Postulate. The situation with join and intersection is not that straightforward. In pa...

An Affine Invariant Local Ternary Patterns Method

Local Binary Patterns and various derivatives of the method have been widely used in the field of texture recognition over the past 15 years. A restriction of these methods is their variance with respect to affine transformations of an image. This is caused by the fixed circular neighborhood and the fixed support area of sampling points. The main approach to deal with affine transformations suc...

Affine and projective planes

Mubs Inequivalence and Affine Planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C for various prime powers N . The number of such sets is not bounded above by any polynomial as a function of N . While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large...

Ordered Rings and Fields