Abstract We resolve Schinzel’s Hypothesis (H) for $$100\%$$ 100 % of polynomials arbitrary degrees. deduce that a positive proportion diagonal conic bundles over $${\mathbb {Q}}$$ Q with any given number degenerate fibres have rational point, and obtain...

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences {PdCn)} and {qd(n)}, and prove that the Makowski &. Schinzel conjecture hold for the sequences {pd(n)} and {qd(n)}.

Filredi, Z. and P. Hajnal, Davenport-Schinzel theory of matrices, Discrete Mathematics 103 (1992) 233-251. Let C be a configuration of 1’s. We define f(n; C) to be the maximal number of l’s in a O-l matrix of size n x n not having C as a subconfiguration. We consider the problem of determining the order off (n; C) for several forbidden C’s. Among other results we prove that f (n; (’ 1 ’ J) = @(...

A generalized Davenport-Schinzel sequence is one over a finite alphabet that contains no subsequences isomorphic to a fixed forbidden subsequence. One of the fundamental problems in this area is bounding (asymptotically) the maximum length of such sequences. Following Klazar, let Ex(σ, n) be the maximum length of a sequence over an alphabet of size n avoiding subsequences isomorphic to σ. It ha...

how to cite this article: singhal r, pandit s, saini a, singh p, dhawan n. the acrocallosal syndrome in a neonate with further widening of phenotypic expression. iran j child neurol. 2014 spring;8(2):60-64.   the presentation of the typical characteristics of the acrocallosal syndrome (acls) are hypoplasia/agenesis of corpus callosum, moderate to severe mental retardation, characteristic cranio...