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

Collins functions for pions from SIDIS and new e+e- data: a first glance at their transverse momentum dependence

New data from Belle and BaBar Collaborations on azimuthal asymmetries, measured in e+e- annihilations into pion pairs at Q^2=112 GeV^2, allow to take the first, direct glance at the transverse momentum dependence of the Collins functions, in addition to their z dependence. These data, together with available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins asymmetry, are simultaneously analysed in the framework of the generalised parton model assuming two alternative Q^2 evolution schemes and exploiting two different parameterisations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e+e- annihilations into pion pairs at the lower Q^2 of 13 GeV^2, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse momentum dependent evolution effects.Comment: 20 pages, 15 figures, 4 table

HERA-B Framework for Online Calibration and Alignment

This paper describes the architecture and implementation of the HERA-B framework for online calibration and alignment. At HERA-B the performance of all trigger levels, including the online reconstruction, strongly depends on using the appropriate calibration and alignment constants, which might change during data taking. A system to monitor, recompute and distribute those constants to online processes has been integrated in the data acquisition and trigger systems.Comment: Submitted to NIM A. 4 figures, 15 page

Sensitive protein detection using an optical fibre long period grating sensor anchored with silica core gold shell nanoparticles

Copyright ©2014 Society of Photo-Optical Instrumentation Engineers. This paper was published in the Proceedings of SPIE and is made available with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.An optical fibre long period grating (LPG), modified with a coating of silica gold (SiO2:Au) core/shell nanoparticles (NPs) deposited using the layer-by-layer (LbL) method, was employed for the development of a bio-sensor. The SiO2:Au NPs were electrostatically assembled onto the LPG with the aid of a poly(hydrochloride ammonium) (PAH) polycation layer. The LPG sensor operates at the phase matching turning point to provide the highest sensitivity. The SiO2:Au NPs were modified with biotin, which was used as a ligand for streptavidin (SV) detection. The sensing mechanism is based on the measurement of the refractive index change induced by the binding of the SV to the biotin. The lowest detected concentration of SV was 19 nM using an LPG modified with a 3 layer (PAH/SiO2:Au) thin film

Simultaneous reweighting of Transverse Momentum Dependent distributions

The Bayesian reweighting procedure is extended to the case of multiple independent extractions of transverse momentum dependent parton distributions (TMDs). By exploiting the data on transverse single spin asymmetries, AN , for inclusive pion production in polarized proton-proton collisions measured at RHIC, we perform a simultaneous reweighting of the quark Sivers, transversity and Collins TMD functions extracted from semi-inclusive deep inelastic scattering (SIDIS) and e+e− annihilation into hadron pairs. The impact of the implementation of the Soffer bound, as well as the differences between older and newer AN data, are investigated. The agreement with AN data at large-xF values, a kinematical region complementary to those explored in SIDIS measurements, is enhanced, improving the knowledge of the polarized quark TMDs in the large-x region

Reweighting the Sivers function with jet data from STAR

The reweighting procedure that using Bayesian statistics incorporates the information contained in a new data set, without the need of re-fitting, is applied to the quark Sivers function extracted from Semi-Inclusive Deep Inelastic Scattering (SIDIS) data. We exploit the recently published single spin asymmetry data for the inclusive jet production in polarized pp collisions from the STAR Collaboration at RHIC, which cover a much wider x region compared to SIDIS measurements. The reweighting method is extended to the case of asymmetric errors and the results show a remarkable improvement of the knowledge of the quark Sivers function

Relativistic Compact Objects in Isotropic Coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho$ is discussed in detail.Comment: 9 pages, no figures, accepted for publication in Pramana-Journal of Physic

Comparative Study on Anterior Cruciate Ligament Reconstruction: Determination of Isometric Points with and Without Navigation

OBJECTIVES: To compare the accuracy of tunnel placement and graft isometry for anterior cruciate ligament reconstruction performed using a computer-assisted navigation system (Orthopilot) and using traditional instruments. METHODS: The anterior cruciate ligament was removed intact from 36 pairs of human cadaver knees. From each pair, one knee was randomized to Group 1 (conventional) and the other to Group 2 (Orthopilot). An inelastic suture was then passed through the central points of the tibial and femoral tunnels. Neither of the tunnels was drilled. All knees were then dissected, and six parameters were obtained: distances from the tibial tunnel center to the 1) posterior cruciate ligament, 2) anterior horn of the lateral meniscus and 3) medial tibial spine; 4) distance from the femoral tunnel center to the posterior femoral cortex; 5) femoral tunnel coronal angle; and 6) variation of the distance from the femoral to the tibial tunnel with the knee extended and at 90 degrees of flexion. RESULTS: The variation of the distance from the femoral to the tibial tunnel during flexion and extension was smaller in the Orthopilot group (better isometry) compared to the conventional group. There were no statistical differences in any other parameters between the groups, and all tunnels were considered to be in satisfactory positions. DISCUSSION: The results obtained for anterior cruciate ligament reconstruction depend on precise isometric point positioning, and a navigation system is a precision tool that can assist surgeons in tunnel positioning. CONCLUSION: No differences in tunnel position were observed between the groups. Nonetheless, better isometry was achieved in the Orthopilot group than with conventional instruments