We study the question of finding the maximal determinant of matrices of odd order with entries ±1. The most general upper bound on the maximal determinant, due to Barba, can only be achieved when the order is the sum of two consecutive squares. It is conjectured that the bound is always attained in such cases. Apart from these, only in orders 3, 7, 9, 11, 17 and 21 has the maximal value been es...

Let n be an ordinal number, let L be an add-associative right complementable right zeroed unital distributive non empty double loop structure, and let m1, m2 be monomials of n, L. Note that m1 ∗m2 is monomial-like. Let n be an ordinal number, let L be an add-associative right complementable right zeroed distributive non empty double loop structure, and let c1, c2 be constant polynomials of n, L...

Viruses catch a wave cientists know from looking at fixed cells that viruses frequently associate with filopodia and microvilli. Using video microscopy, Lehmann et al. (page 317) find that after a virus attaches to the filopodial membrane, it surfs down the plasma membrane toward the cell body. Entry into the cell occurs only after the virus has reached the base of the filopodium. Retroviruses ...

Ultrafast photochromic molecules are being actively investigated to meet the demand for fast optical switching systems. Inspired on irreversible cyclization of 9-phenylphenalenone plant metabolites yield highly-coloured naphthoxanthenes purpose defense against pathogens, aryl-substituted phenalenones have been developed that undergo a similar but reversible reaction. The lifetime naphthoxanthen...

Let F={P1,...,Pm} be a family of sets. A partial order P(F, <) on F is naturally defined by the condition Pi< Pj iff Pi is contained in Pj. When the elements of F are disks (i.e. circles together with their interiors), P(F, <) is called a circle order; if the elements of F are n-polygons, P(F, <) is called an n-gon order. In this paper we study circle orders and n-gon orders. The crossing numbe...

Rational Chebyshev approximations are given for the complete Fermi-Dirac integrals of orders — \, \ and f. Maximal relative errors vary with the function and interval considered, but generally range down to 10~9 or less.

Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying link behind all these orders has been shown that links them to well-known graph decompositions into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying conce...