An amicable pair for an elliptic curve E/Q is a pair of primes (p, q) of good reduction for E satisfying #Ẽp(Fp) = q and #Ẽq(Fq) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j 6= 0) have no aliqout cycles of length greate...

in this paper, analysis of fluid flow and heat transfer over the bank of tubes is considered. k-ω sst model is applied for simulation of turbulent flow. in this paper, the improvement of efficiency of a bundle of circular tubes by changing the shape of the cross section of one row of the pipes to the elliptical cross section as an innovative plan is considered. as know, friction factor in turbu...

a modified model has been analytically developed to describe the induction time of an elliptic air bubble in contact with an elliptic hydrophobic oil droplet. the role of hydrophobicity was revealed in the slippage of liquid over the surfaces of bubble and droplet. in this condition, the analytical relationships for pressure distribution and consequently hydrodynamic resistance force through th...

Understanding the effects of defects is crucial due to their deliberate or unintentional presence in many materials. Classical theory elasticity may not be best candidate describe behaviour structures with comparable size its underlying material organization, as it lacks internal scale parameters. In this respect, present study focused on comparison two well-established non-local theories; ‘imp...

advanced metering infrastructure (ami) is a key part of the smart grid; thus, one of the most important concerns is to offer a secure mutual authentication.  this study focuses on communication between a smart meter and a server on the utility side. hence, a mutual authentication mechanism in ami is presented based on the elliptic curve cryptography (ecc) and one time signature (ots) consists o...

In this paper, the stress concentration around a hole in the single layer composite materials with long fibers is examined. The single layer has an infinite length, limited with and instant thickness and is loaded by a constant tension force p at infinity. The width of the lamina is considered to be finite and bears a hole as a defect. Due to presence of excessive shear stress in the matrix bay...

In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...

Elliptic curves in Hesse form admit more suitable arithmetic than ones in Weierstrass form. But elliptic curve cryptosystems usually use Weierstrass form. It is known that both those forms are birationally equivalent. Birational equivalence is relatively hard to compute. We prove that elliptic curves in Hesse form and in Weierstrass form are linearly equivalent over initial field or its small e...