Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GENERATING FUNCTION FOR CLEBSCH-GORDAN-COEFFICIENTS, OF THE SUQ(2) QUANTUM ALGEBRA

Some methods have been developed to calculate the su(q)(2) Clebsch-Gordan coefficients (CGC). Here we develop a method based on the calculation of Clebsch-Gordan generating functions through the use of 'quantum algebraic' coherent states. Calculating the su(q)(2) CGC by means of this generating function is an easy and straightforward task.

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

Analysis of diametrical wear of grinding wheel and roundness errors in the machining of steel VC 131

Due to the high industrial competitiveness, the rigorous laws of environmental protection, the necessary reduction of costs, the mechanical industry sees itself forced to worry more and more with the refinement of your processes and products. In this context, can be mentioned the need to eliminate the roundness errors that appear after the grinding process. This work has the objective of verifying if optimized nozzles for the application of cutting fluid in the grinding process can minimize the formation of the roundness errors and the diametrical wear of grinding wheel in the machining of the steel VC 131 with 60 HRc, when compared to the conventional nozzles. These nozzles were analyzed using two types of grinding wheels and two different cutting fluids. Was verified that the nozzle of 3mm of diameter, integral oil and the CBN grinding wheel, were the best options to obtain smaller roundness errors and the lowest diametrical wears of grinding wheels.

Eigenvalue analyses of two parallel lines using a single real transformation matrix

For a typical non-symmetrical system with two parallel three phase transmission lines, modal transformation is applied using some examples of single real transformation matrices. These examples are applied searching an adequate single real transformation matrix to two parallel three phase transmission line systems. The analyses are started with the eigenvector and eigenvalue studies, using Clarke's transformation or linear combinations of Clarke's elements. The Z C and parameters are analyzed for the case that presents the smallest errors between the exact eigenvalues and the single real transformation matrix application results. The single real transformation determined for this case is based on Clarke's matrix and its main characteristic is the use of a unique homopolar reference. So, the homopolar mode becomes a connector mode between the two three-phase circuits of the analyzed system. ©2005 IEEE.

Modeling approach based on experimental results for prediction of measurement errors in energy meters

This paper presents a general modeling approach to investigate and to predict measurement errors in active energy meters both induction and electronic types. The measurement error modeling is based on Generalized Additive Model (GAM), Ridge Regression method and experimental results of meter provided by a measurement system. The measurement system provides a database of 26 pairs of test waveforms captured in a real electrical distribution system, with different load characteristics (industrial, commercial, agricultural, and residential), covering different harmonic distortions, and balanced and unbalanced voltage conditions. In order to illustrate the proposed approach, the measurement error models are discussed and several results, which are derived from experimental tests, are presented in the form of three-dimensional graphs, and generalized as error equations. © 2009 IEEE.

Evaluation of measurement errors of temperature and relative humidity from HOBO data logger under different conditions of exposure to solar radiation

This study aimed to assess measurements of temperature and relative humidity obtained with HOBO a data logger, under various conditions of exposure to solar radiation, comparing them with those obtained through the use of a temperature/relative humidity probe and a copper-constantan thermocouple psychrometer, which are considered the standards for obtaining such measurements. Data were collected over a 6-day period (from 25 March to 1 April, 2010), during which the equipment was monitored continuously and simultaneously. We employed the following combinations of equipment and conditions: a HOBO data logger in full sunlight; a HOBO data logger shielded within a white plastic cup with windows for air circulation; a HOBO data logger shielded within a gill-type shelter (multi-plate prototype plastic); a copper-constantan thermocouple psychrometer exposed to natural ventilation and protected from sunlight; and a temperature/relative humidity probe under a commercial, multi-plate radiation shield. Comparisons between the measurements obtained with the various devices were made on the basis of statistical indicators: linear regression, with coefficient of determination; index of agreement; maximum absolute error; and mean absolute error. The prototype multi-plate shelter (gill-type) used in order to protect the HOBO data logger was found to provide the best protection against the effects of solar radiation on measurements of temperature and relative humidity. The precision and accuracy of a device that measures temperature and relative humidity depend on an efficient shelter that minimizes the interference caused by solar radiation, thereby avoiding erroneous analysis of the data obtained.

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Flattening of the resonance spectrum of hadrons from κ-deformed Poincaré algebra

Recently Lukierski et al. [1] defined a κ-deformed Poincaré algebra which is characterized by having the energy-momentum and angular momentum sub-algebras not deformed. Further Biedenharn et al. [2] showed that on gauging the κ-deformed electron with the electromagnetic field, one can set a limit on the allowed value of the deformation parameter ∈ ≡ 1/κ < 1 fm. We show that one gets Regge like angular excitations, J, of the mesons, non-strange and strange baryons, with a value of ∈ ∼ 0.082 fm and predict a flattening with J of the corresponding trajectories. The Regge fit improves on including deformation, particularly for the baryon spectrum.

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

ON THE RADICAL OF A FREE MALCEV ALGEBRA

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Characterization of electromagnetic fields in the aSPECT spectrometer and reduction of systematic errors

Das aSPECT Spektrometer wurde entworfen, um das Spektrum der Protonen beimrnZerfall freier Neutronen mit hoher Präzision zu messen. Aus diesem Spektrum kann dann der Elektron-Antineutrino Winkelkorrelationskoeffizient "a" mit hoher Genauigkeit bestimmt werden. Das Ziel dieses Experiments ist es, diesen Koeffizienten mit einem absoluten relativen Fehler von weniger als 0.3% zu ermitteln, d.h. deutlich unter dem aktuellen Literaturwert von 5%.rnrnErste Messungen mit dem aSPECT Spektrometer wurden an der Forschungsneutronenquelle Heinz Maier-Leibnitz in München durchgeführt. Jedoch verhinderten zeitabhängige Instabilitäten des Meßhintergrunds eine neue Bestimmung von "a".rnrnDie vorliegende Arbeit basiert hingegen auf den letzten Messungen mit dem aSPECTrnSpektrometer am Institut Laue-Langevin (ILL) in Grenoble, Frankreich. Bei diesen Messungen konnten die Instabilitäten des Meßhintergrunds bereits deutlich reduziert werden. Weiterhin wurden verschiedene Veränderungen vorgenommen, um systematische Fehler zu minimieren und um einen zuverlässigeren Betrieb des Experiments sicherzustellen. Leider konnte aber wegen zu hohen Sättigungseffekten der Empfängerelektronik kein brauchbares Ergebnis gemessen werden. Trotzdem konnten diese und weitere systematische Fehler identifiziert und verringert, bzw. sogar teilweise eliminiert werden, wovon zukünftigernStrahlzeiten an aSPECT profitieren werden.rnrnDer wesentliche Teil der vorliegenden Arbeit befasst sich mit der Analyse und Verbesserung der systematischen Fehler, die durch das elektromagnetische Feld aSPECTs hervorgerufen werden. Hieraus ergaben sich vielerlei Verbesserungen, insbesondere konnten die systematischen Fehler durch das elektrische Feld verringert werden. Die durch das Magnetfeld verursachten Fehler konnten sogar soweit minimiert werden, dass nun eine Verbesserung des aktuellen Literaturwerts von "a" möglich ist. Darüber hinaus wurde in dieser Arbeit ein für den Versuch maßgeschneidertes NMR-Magnetometer entwickelt und soweit verbessert, dass nun Unsicherheiten bei der Charakterisierung des Magnetfeldes soweit reduziert wurden, dass sie für die Bestimmung von "a" mit einer Genauigkeit von mindestens 0.3% vernachlässigbar sind.