We develop the theory of Abelian functions defined using a tetragonal curve of genus six, with the specific example of the cyclic curve, y = x + λ4x + λ3x + λ2x + λ1x + λ0 discussed in detail. We define generalisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the associated partial differential equations satisfied by the f...

Let C be a curve of genus g over a field k. We describe probabilistic algorithms for addition and inversion of the classes of rational divisors in the Jacobian of C. After a precomputation, which is done only once for the curve C, the algorithms use only linear algebra in vector spaces of dimension at most O(g log g), and so take O(g3+ ) field operations in k, using Gaussian elimination. Using ...

A new GF(p) cryptographic processor architecture for elliptic curve encryption/decryption is proposed in this paper. The architecture takes advantage of projective coordinates to convert GF(p) inversion needed in elliptic point operations into several multiplication steps. Unlike existing sequential designs, we show that projecting into (X/Z,Y/Z) leads to a much better improved performance than...

In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) McCulloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and...

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves ...

tehran, the capital of iran, is under the threat of large magnitude earthquakes (above 7) located on known active faults. previous studies on the effect of local surface geology on earthquake ground motion using 1d calculation of sh transfer function (jafari et al., 2001; jica & cest, 2000) and using experimental methods (haghshenas, 2005) based on earthquake and ambient noise vibration recordi...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

An experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, CCl4/water, toluene /water + glycerol (25 % wt), toluene + CCl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. The effects of physical properties, mass transfer and column geometry...

Ground Penetrating Radar (GPR) has found widespread application for the non-invasive characterization of the subsurface. Nevertheless, the interpretation of GPR measurements remains difficult in some cases, particularly when the subsurface contains thin horizontal layers with contrasting dielectric properties that might act as waveguides for electromagnetic wave propagation. GPR data affected b...

Introduction: Look-Locker inversion recovery produces images at multiple inversion times (TI) after a 180° inversion pulse (1). In non-cardiac and phantom experiments, the sequence timing can be carefully controlled. This allows the user to exactly specify both the TIs and the magnetization recovery time between inversions. In cardiac imaging, however, these timing variables are measured in uni...