Given an abelian group G, it is natural to ask whether there exists a permutation π of G that “destroys” all nontrivial 3-term arithmetic progressions (APs), in the sense that π(b)− π(a) 6= π(c)−… (More)

Localised pin-hole type corrosion defects affecting the structural stability of pipes is a serious challenge faced by the oil and gas industry. The problem is even more severe at support locations… (More)

Let E be an elliptic curve over Q, and for each prime p, let #E(Fp) be the number of rational points of E over the finite field Fp. Taking aE(p) = p+ 1−#E(Fp) to be the trace of Frobenius as usual,… (More)

Herbicide mixtures are commonly used in agriculture to broaden the spectrum of weed control. The interactions or the combinations may be desirable or undesirable. Acetachlor at 150g/ha applied and… (More)

In this article, we show that in each of four standard families of hyperelliptic curves, there is a density-1 subset of members with the property that their Jacobians have adelic Galois… (More)

Let I ⊂ N be an infinite subset, and let {a i } i∈I be a sequence of nonzero real numbers indexed by I such that there exist positive constants m, C 1 for which |a i | ≤ C 1 · i m for all i ∈ I.… (More)

For a positive integer g, let Sp2g(R) denote the group of 2g × 2g symplectic matrices over a ring R. Assume g ≥ 2. For a prime number , we give a self-contained proof that any closed subgroup of… (More)

Humic acid typically contains heterocyclic compowx:\s with carboxylic, phenolic, alcoholic and carbonyl fractions extracted from lignite with high molecular weight. Humic acid has been extracted from… (More)

Let E1 and E2 be Q-nonisogenous, semistable elliptic curves over Q, having respective conductors NE1 and NE2 and both without complex multiplication. For each prime p, denote by aEi(p) := p+1−#Ei(Fp)… (More)

Cotton, the "King of fibres" is often quoted as •White gold' because of its higher commercial value. Our country ranks first in cotton acreage but the productivity is less. One of the major… (More)