Fractional Newton-Raphson Method Accelerated with Aitken's Method

The Newton-Raphson (N-R) method is characterized by the fact that generating a divergent sequence can lead to the creation of a fractal, on the other hand the order of the fractional derivatives seems to be closely related to the fractal dimension, based on the above, a method was developed that makes use of the N-R method and the fractional derivative of Riemann-Liouville (R-L) that has been named as the Fractional Newton-Raphson (F N-R) method. In the following work we present a way to obtain the convergence of the F N-R method, which seems to be at least linearly convergent for the case where the order $\alpha$ of the derivative is different from one, a simplified way to construct the fractional derivative and fractional integral operators of R-L is presented, an introduction to the Aitken's method is made and it is explained why it has the capacity to accelerate the convergence of iterative methods to finally present the results that were obtained when implementing the Aitken's method in F N-R method.Comment: Newton-Raphson Method, Fractional Calculus, Fractional Derivative of Riemann-Liouville, Method of Aitken. arXiv admin note: substantial text overlap with arXiv:1710.0763

On the Design of Cryptographic Primitives

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed

Nitrogen and carbon isotope composition of organic Fertilizers.

Synthetic (e.g. urea) and organic fertilizers (e.g. compost) differed markedly in N isotope composition and the greater the difference between organic and synthetic fertilizer the more robust will be the differentiation of crops and vegetable grown under different farming systems. The objective of this study was to compare nitrogen and carbon isotope composition of organic fertilizers and manures available for conventional and organic farming in Brazil. Seven samples of organic fertilizer, two of organo-mineral fertilizers and two of different animal manures were analyzed for nitrogen and carbon isotope composition (15N, 13C). Organic fertilizers and manure samples were enriched in 15N as expected. Using synthetic fertilizers as the primary material of organo-mineral fertilizer can imprint a low 15N value to the final product. Organic fertilizers, organo-mineral fertilizers and manures can have their organic feedstock differentiated using 13C. These are preliminary data of the isotopic composition of organic fertilizer in Brazil. Therefore, a wider survey of fertilizers and an experimental approach for organic- and organo-mineral fertilizer production is needed to elucidate the natural isotope variation of the array of available products

Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography

Quantum state reconstruction involves measurement devices that are usually described by idealized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.Comment: 11 pages, 3 figure

Preparation and structural properties of thin films and multilayers of the Heusler compounds Cu2MnAl, Co2MnSn, Co2MnSi and Co2MnGe

We report on the preparation of thin films and multilayers of the intermetallic Heusler compound CuMnAl, Co2MnSn, Co2MnSi and Co2MnGe by rf-sputtering on MgO and Al2O3 substrates. Cu2MnAl can be grown epitaxially with (100)-orientation on MgO (100) and in (110)-orientation on Al2O3 a-plane. The Co based Heusler alloys need metallic seedlayers to induce high quality textured growth. We also have prepared multilayers with smooth interfaces by combining the Heusler compounds with Au and V. An analysis of the ferromagnetic saturation magnetization of the films indicates that the Cu2MnAl-compound tends to grow in the disordered B2-type structure whereas the Co-based Heusler alloy thin films grow in the ordered L21 structure. All multilayers with thin layers of the Heusler compounds exhibit a definitely reduced ferromagnetic magnetization indicating substantial disorder and intermixing at the interfaces.Comment: 21 pages, 8 figure