Perpendicular orders

On Perpendicular Texture

or: Why do we see more owers in the distance? Abstract Almost all work on texture in the computer vision and graphics communities has modeled the texture as tangential, i.e. lying in the tangent plane to the surface. This is equivalent to thinking of the texture as a pattern painted on the surface. Three-dimensional textures, where the elements may point out of the surface , have largely been i...

On orders induced by implications

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

Perpendicular Dissections of Space

For each pair (Qi, Qj) of reference points and each real number r there is a unique hyperplane h ⊥ QiQj such that d(P,Qi)2 − d(P,Qj)2 = r for points P in h. Take n reference points in d-space and for each pair (Qi, Qj) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure of the semilattice of intersections of the hyperplanes...

Theory of Perpendicular Arrays

Converse Lagrange Theorem Orders and Supersolvable Orders

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...