We give a slight improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval with a fixed integral. Also, by means of explicit examples we disprove a long standing natural conjecture of Schinzel and Schmidt concerning the extremal function for such autoconvolutions. 2000 Mathematics Subject Classification. Primary 42A85...

We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-s double DS sequences, for all s, sharp bounds on sequences avoiding catenated permutations (aka formation free sequences), and new lower bounds on sequences avoiding zig-zagging patterns.

An (n; s) Davenport{Schinzel sequence, for positive integers n and s, is a sequence composed of n distinct symbols with the properties that no two adjacent elements are equal, and that it does not contain, as a (possibly non-contiguous) subsequence, any alternation a b a b of length s + 2 between two distinct symbols a and b. The close relationship between Davenport{Schinzel sequences and the c...

this study was conducted to evaluate the quality of the red flesh apples and golab cultivars. two iranian red flesh apples from shahroud and four golab cultivars as well as ‘gala’ as control from damavand were selected in summer 2012. fruit physical characteristics including length, diameter, fresh weight and dry weight, firmness, color and their parameters were evaluated for each cultivar. the...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...