In this paper we study structures related to torsion of elliptic curves defined over number fields. The aim is to build families of elliptic curves more efficient to help factoring numbers of special form, including numbers from the Cunningham Project. We exhibit a family of curves with rational Z/4Z×Z/4Z torsion and positive rank over the field Q(ζ8) and a family of elliptic curves with ration...

We show here how to construct bases of the Z-module Int(P,Z) of polynomials that are integer-valued on the prime numbers together with their finite divided difference, that is, Int(P,Z) = { f ∈ Q[x] | ∀p, q ∈ P f(p) ∈ Z and f(p)− f(q) p− q ∈ Z } .

PURPOSE This study was performed to investigate the accuracies of the synthesized monochromatic images and effective atomic number maps obtained with the new GE Discovery CT750 HD CT scanner. METHODS A Gammex-RMI model 467 tissue characterization phantom and the CT number linearity section of a Phantom Laboratory Catphan 600 phantom were scanned using the dual energy (DE) feature on the GE CT...

Schur's inequality for the sum of products differences real numbers states that $x,y,z,t\geq 0$, $x^t(x-y)(x-z) + y^t(y-z)(y-x) z^t(z-x)(z-y) \geq 0$. In this paper we study a generalization to more terms, general functions variables and algebraic structures such as vectors Hermitian matrices.

A new approach to sustainable project scheduling for public institutions is proposed. The based on experts’ opinions three aspects of sustainability activities (human resources consumption, material consumption and negative influence local communities), expressed by means Z-fuzzy numbers. fuzzy bicriterial optimization model proposed, whose objective obtain a schedule an acceptable degree durat...

The Z-number is a new fuzzy-theoretic concept, proposed by Zadeh in 2011. It extends the basic philosophy of Computing With Words (CWW) to include the perception of uncertainty of the information conveyed by a natural language statement. The Z-number thus, serves as a model of linguistic summarization of natural language statements, a technique to merge human-affective perspectives with CWW, an...

We deene a new height function R (), the Remak height of an algebraic number. We give sharp upper and lower bounds for R () in terms of the classical Mahler measure M () : Study of when one of these bounds is exact leads us to consideration of conjugate sets of algebraic numbers of norm 1 lying on two circles centered at 0. We give a complete characterisation of such conjugate sets. They turn o...