— Let E be an elliptic curve defined over a number field F and K/F a quadratic extension. For a point P ∈ E(F) that is a local trace for every completion of K/F, we find necessary and sufficient conditions for P to lie in the image of the global trace map. These conditions can then be used to determine whether a quadratic twist of E, as a genus one curve, has rational points. In the case of qua...

This paper provides a new answer to the old problem of specifying the mixed partial derivatives (MPDs) or ‘twist vectors’ at the grid points for an interpolating surface over a rectangular network of curves. An algorithm is presented for finding the MPDs that minimizes a generalized energy integral over the entire surface. The integrand may be any quadratic form in the second partial derivative...

We describe an implementation of fast elliptic curve scalar multiplication, optimized for Diffie–Hellman Key Exchange at the 128-bit security level. The algorithms are compact (using only x-coordinates), run in constant time with uniform execution patterns, and do not distinguish between the curve and its quadratic twist; they thus have a built-in measure of sidechannel resistance. The core of ...

We consider two new classes of twisted D=4 quantum Poincaré symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate the two-parameter class of twisted Poincaré algebras which provide the Liealgebraic noncommutativity of the translations. The corresponding star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the...

In this paper, we investigate the properties of well-rounded twists a given ideal lattice an imaginary quadratic field [Formula: see text]. We show that every text] has at least one twist lattice. Moreover, provide explicit algorithm to compute all

Incorrect formulation and incorrect solution of the problem CSIDH algorithm implementation on Edwards curves was revealed in one famous works. The purpose this paper is to present a detailed critique such concept with proof its inconsistency. Specific properties three non-isomorphic classes super singular generalized form are considered: full, quadratic, twisted curves. Conditions for existence...

The present study performs a set of static tests to demonstrate novel passive morphing concept. concept introduces bend–twist coupled composite spar rotor blades, allowing for twist be achieved by imposing lagwise bending moment using centrifugal forces produced movable mass at the blade tip. First, three spars are fabricated symmetric layup configuration with varied ply orientations. A designe...

Introduction Left ventricular (LV) twist is believed to store potential energy and plays an important role in generating diastolic suction. Recent advances in echocardiography techniques have allowed quantification of LV twist. The aim of the present study was to compare LV twist and torsion in healthy human subjects determined by velocity vector imaging (VVI) and tissue Doppler imaging (TDI) a...