2014 Methods to deduce the parameters of a multilayer X-ray mirror from its reflectivity curve are reviewed. Inversion methods are successful for coatings with few layers and give the thickness of each layer and the roughness of each interface. A statistical description of the coating is used for coatings with many layers, and simple formulas are given to derive the average thickness error and ...

A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods. Two procedures to choose the strength of the regularisation are tested, namely the L-curve scan and a scan of global correlation coefficients. The advantage...

The paper describes FPGA implementation of cryptographic coprocessor performing operations on elliptic curve points with coordinates in GF (2). Polynomial basis and normal basis arithmetic units are presented and compared. Hardware implementation of GCD inversion in polynomial basis is described. Where an optimal normal basis exists, the normal basis arithmetic performs better. The digit width ...

in this paper we proposed a new approach to divisor scalar multiplication in Jacobian of genus 2 hyperelliptic curves over fields with odd characteristic, without field inversion. It is based on improved addition formulae of the weight 2 divisors in projective divisor representation in most frequent case that suit very well to scalar multiplication algorithms based on Euclidean addition chains....

This paper presents faster inversion-free point addition formulas for the curve y(1 + ax) = cx(1 + dy). The proposed formulas improve the point doubling operation count record from 6M + 5S to 8M and mixed addition operation count record from 10M to 8M. Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of 2M per either of the group operations.

The paper describes FPGA implementation of cryptographic coprocessor performing operations on elliptic curve points with coordinates in GF (2). Polynomial basis and normal basis arithmetic units are presented and compared. Hardware implementation of GCD inversion in polynomial basis is described. Where an optimal normal basis exists, the normal basis arithmetic performs better. The digit width ...

Introduction: Quantitative magnetic resonance imaging is a powerful tool for investigating a large variety of biological phenomena. Thus, big efforts have been made during the recent years in order to develop fast methods for the quantitative assessment of various MR parameters. Two very important parameters are the T1 and T2* relaxation times. Here a new method for the simultaneous measurement...

One of the most remarkable basis of the gravity data inversion is the recognition of sharp boundaries between an ore body and its host rocks during the interpretation step. Therefore, in this work, it is attempted to develop an inversion approach to determine a 3D density distribution that produces a given gravity anomaly. The subsurface model consists of a 3D rectangular prisms of known sizes ...

Large-scale magnetic field configurations are important for the transport of solar wind strahl electrons, which are suprathermal and directed along the field outward from the Sun. Strahl electrons are routinely used to infer not only the field configurations between the Sun and Earth but also local field structures, i.e., field inversions, where the magnetic field is locally folded back or inve...

The security of pairing-based cryptosystems is closely related to the difficulty of the pairing inversion problem(PI). In this paper, we discuss the difficulty of pairing inversion on the generalized ate pairings of Vercauteren. First, we provide a simpler approach for PI by generalizing and simplifying Kanayama-Okamotos approach; our approach involves modifications of exponentiation inversion(...