The multiplier spectral curve of a conformal torus f : T 2 → S in the 4– sphere is essentially [3] given by all Darboux transforms of f . In the particular case when the conformal immersion is a Hamiltonian stationary torus f : T 2 → R in Euclidean 4–space, the left normal N : M → S of f is harmonic, hence we can associate a second Riemann surface: the eigenline spectral curve of N , as defined...

As computing and communication devices are equipped with increasingly versatile wireless connection capabilities, the demand for security increases. Cryptography provides a method for securing and authenticating the transmission of information over the insecure channels. Elliptic Curve [EC] Cryptography is a public key cryptography which replaces RSA because of its increased security with lesse...

Abstract The roughness of the joint surface plays a significant role in evaluating shear strength rock. waviness (first-order) and unevenness (second-order) natural joints have different effects on characterization roughness. To accurately quantify influence two-order asperity coefficient (JRC) prediction profile curve, optimal sampling interval was determined through change <m:math xmlns:m="ht...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

We prove that the minimal free resolution of secant variety a curve is asymptotically pure. As corollary, we show Betti numbers converge to normal distribution.

| Finite eld arithmetic is becoming increasingly important in cryptographic applications. In particular cryptographic primitives based on the discrete logarithm problem over elliptic curve groups are accomplished essentially by arithmetic in nite elds. It is well known that the ef-ciency of nite eld arithmetic depends strongly on the particular way in which the eld elements are represented. The...