It is well known that the regular continued fraction expansion of a quadratic irrational is symmetric about its centre; we refer to this symmetry as horizontal. However, an additional vertical symmetry is exhibited by the continued fraction expansions arising from a family of quadratics known as Schinzel sleepers. This paper provides a method for generating every Schinzel sleeper and investigat...

Definition 18.1 A (n, s)-Davenport-Schinzel sequence is a sequence over an alphabet A of size n in which no two consecutive characters are the same and there is no alternating subsequence of the form .

Abstract We establish a version “over the ring” of celebrated Hilbert Irreducibility Theorem. Given finitely many polynomials in k + n {k+n} variables, with coefficients ? {\mathbb{Z}} , positive degree last n we show that if they are irreducible over and satisf...

Davenport-Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport-Schinzel sequence composed of n symbols is 6(noc(n»), where t1.(n)is the functional inverse of Ackermann's function, and is thus very slowly increasing to infinity. This i...

to determine the phenolic content and antioxidant activity in some native iranian apple cultivars, some five cultivars namely: 'bekran', 'golab-e kermanshah', 'golab-e kohanz' 'golab-e sheikhi' and 'atlasi' were selected and compared with the standard cultivar 'gala'. the profiles related to four phenolic compounds (chlorogenic acid, quercetin-3-galactoside, catechin, and phloridzin) were deter...

We give a Schinzel-Zassenhaus-type lower bound for the maximum modulus of roots monic integer polynomial with all symmetric respect to unit circle. Our results extend recent work Dimitrov, who proved general Schinzel-Zassenhaus conjecture by using Pólya rationality theorem power series coefficients, and some estimates logarithmic capacity (transfinite diameter) sets. use an enhancement Pólya's ...