In this paper, we enumerate the number of combinatorial changes of the the Euclidean minimum spanning tree (EMST) of a set of n moving points in 2dimensional space. We assume that the motion of the points in the plane, is defined by algebraic functions of maximum degree s of time. We prove an upper bound of O(nβ2s(n )) for the number of the combinatorial changes of the EMST, where βs(n)=λs(n)/n...

We introduce a containment relation of hypergraphs which respects linear orderings of vertices and investigate associated extremal functions. We extend, by means of a more generally applicable theorem, the n log n upper bound on the ordered graph extremal function of F = ({1, 3}, {1, 5}, {2, 3}, {2, 4}) due to Füredi to the n(log n)2(log log n)3 upper bound in the hypergraph case. We use Davenp...

We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a lower bound on Mahler’s measure of a polynomial with no cyclotomic factors whose coefficients are all congruent to 1 modulo m for some integer m ≥ 2, raise a lower bound in the problem of Schinzel and Zassenha...

‎two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎levi-civita‎, ‎canonical (zamkovoy)‎, ‎golab and generalized dual‎. ‎their relationship is also analyzed with a special view towards their curvature‎. ‎the particular case of an almost paracosymplectic manifold giv...

Define a covering system (or covering) of the integers as a finite collection of congruences x ≡ aj (mod mj), with 1 ≤ j ≤ r, such that every integer satisfies at least one of these congruences. As an interesting application of coverings, W. Sierpiński [4] showed that there are odd positive integers k for which k · 2 + 1 is composite for all integers n ≥ 0. For d ∈ Z, the first author [1] consi...

in this study, the amount of total phenol, chlorogenic acid, catechin, quercetin, phloridzin, cyanidin and antioxidant activity of apple (malus domestica) skin and flesh of six iranian cultivars, including: ‘golab kohanz’, ‘sib torsh dirras’, ‘ghara yapragh’, ‘torkman’, ‘ghezel alma’ and ‘abbasi mashhad’, and four commercial cultivars including: ‘golden delicious’, ‘red delicious’, ‘braeburn’ a...