We generalize a result of Segre on permutable orthogonal and unitary polarities of PG(2, q) with q odd, by considering non-desarguesian projective planes of odd square order.

In this paper, we consider a repetitive routing problem which we find on a printed circuit board assembly line. There are m different printed circuit boards to be processed. As an automated manipulator embeds electronic parts in a printed circuit board from above, n identical pins from underneath protect it against overbending. A dedicated pin configuration is designed for each printed circuit ...

Let A be an algebra. We use Con(A) to denote the congruence lattice of A. We say that θ, δ ∈ Con(A) permute if θ∨δ = {(x, y) ∈ A: there is z ∈ A such that (x, z) ∈ θ and (z, y) ∈ δ}. The algebra A is congruence permutable (permutable for short) if every pair of congruences in Con(A) permutes. By a system on A we understand a 2n-tuple (θ1, . . . , θn;x1, . . . , xn), where θ1, . . . , θn ∈ Con(A...

Abstract Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type and discuss their operational similarity (SOS) relationships, which are often permutable. A number recent experimental observations, including current-induced magnetization in polar ...

Using some geometry of quadrics permutable with a Hermitian surface H(3, q2) of PG(3, q2), q odd, a class of ovoids of H(3, q2) admitting the group PGL(2, q) is constructed.