In this paper, we study a class of elliptic curves over Q with Qtorsion group Z2×Z2, and prove that the average order of the 2-Selmer groups is bounded.

We show that the average size of subsets of [n] forming an intersecting Sperner family of cardinality not less than ( n−1 k−1 ) is at least k provided that k 6 n=2− √ n=2 + 1. The statement is not true if n=2¿ k ¿n=2−√8n+ 1=8+9=8. c © 2002 Elsevier Science B.V. All rights reserved.

Five image processing algorithms are proposed to measure the average orientation, eccentricity and size of cells in images of biological tissue. These properties, which can be embodied by an elliptical ‘composite cell’, are crucial for biomechanical tissue models. To automatically determine these properties is challenging due to the diverse nature of the image data, with tremendous and unpredic...

Grapevine (Vitis vinifera L.) is one of important economic fruit crops found in Salahaldin province \ Iraq. To examine the Molecular characterization and genetic relationships among nine grape varieties by using random amplified polymorphic DNA (RAPD) marker. Fifteen RAPD primers produced band (71, 56%), while two yielded monomorphic bands only. The size fragment ranged between 250-2700 bp, wit...

We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process wh...

Over the past quarter-century, microbiologists have used DNA sequence information to aid in the characterization of microbial communities. During the last decade, this has expanded from single genes to microbial community genomics, or metagenomics, in which the gene content of an environment can provide not just a census of the community members but direct information on metabolic capabilities ...

Novel amphiphilic poly-N-vinylpyrrolidone derivatives with different molecular weight of hydrophilic PVP fragment and one secondary di-n-alkyl terminal hydrophobic fragment of different length were synthesized to compare their inclination for formation of nano-scaled micelle-like aggregates in aqueous media with previously studied primary n-alkyl terminated poly-N-vinylpyrrolidones. The behavio...

We have evaluated by numerical simulation the average size R(K) of random polygons of fixed knot topology K=,3(1),3(1) musical sharp 4(1), and we have confirmed the scaling law R(2)(K) approximately N(2nu(K)) for the number N of polygonal nodes in a wide range; N=100-2200. The best fit gives 2nu(K) approximately 1.11-1.16 with good fitting curves in the whole range of N. The estimate of 2nu(K) ...

In this paper, the relation between the Glushkov automaton (Apos) and the partial derivative automaton (Apd) of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of Apos was proved by Nicaud to be linear in the size of the corresponding expression. This result was obtained using an upper bound of the number of transitions of Apos. Here ...

This paper explores some structural constraints on computing the mean sizes of sets of elements. Neither number nor density had much effect on judgments of mean size. Intermingled sets of circles segregated only by color gave mean discrimination thresholds for size that were as accurate as sets segregated by location. They were about the same when the relevant color was cued, when it was not cu...