Modal representation of three-phase lines applying two transformation matrices: Evaluation of its eigenvectors

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into Quasi-modes alpha, beta and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a nontransposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km.

Modal representation of three-phase lines applying two transformation matrices: Evaluation of its eigenvectors

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into Quasi-modes α, β and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km. ©2006 IEEE.

Absence of gluonic components in axial and tensor mesons

A quarkonium-gluonium mixing scheme previously developed to describe the characteristic of the pseudoscalar mesons is applied to axial and tensor mesons. The parameters of the model are determined by fitting the eigenvalues of a mass matrix. The corresponding eigenvectors give the proportion of light quarks, strange quarks and glueball in each meson. However, the predictions of the model for the branching ratios and electromagnetic decays are incompatible with the experimental results. These results suggest the absence of gluonic components in the states of axial and tensor isosinglet mesons analyzed here.

Alternative proposal for Modal Representation of a Non-transposed Three-Phase Transmission Line with a Vertical Symmetry Plane

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into quasi-modes a, b and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km.

Fee - fishing operation evaluation at Nothwest São Paulo State, Brazil

Os lagos de pesca recreativa, pesque-pague, surgiram no Brasil em um cenário agrícola denominado como novo rural brasileiro. Este estudo conduzido no noroeste paulista teve como foco o desempenho produtivo dos lagos de pesca recreativa. Foram feitas visitas mensais a nove empreendimentos de pesca recreativa durante seis meses. A cada visita foi aplicado um questionário contendo 13 indicadores de desempenho. Os dados levantados foram submetidos à análise multivariada (MANOVA), análise de componente principal (ACP) e análise de agrupamento. A MANOVA indicou diferenças significativas entre os lagos de pesca recreativa. A ACP revelou, a partir do coeficiente dos autovalores, três atributos: sistema produtivo, gerenciamento pesqueiro e administração operacional. A análise de agrupamento classificou os lagos de pesca recreativa em quatro grupos. Freqüência de pescadores (FP), densidade de estocagem (DE), biomassa de estocagem (BE), captura total (CT) e captura lago dia (CLD), os quais fazem parte do atributo sistema produtivo, mostrando-se os indicadores mais importantes para a avaliação de desempenho dos lagos de pesca recreativa neste estudo.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

Step by step analyses of Clarke's matrix correction procedure for untransposed three-phase transmission line cases

The correction procedure for Clarke's matrix, considering three-phase transmission line analyzes, is analyzed step by step in this paper, searching to improve the application of this procedure. Changing the eigenvectors as modal transformation matrices, Clarke's matrix has been applied to analyses for transposed and untransposed three-phase transmission line cases. It is based on the fact that Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines considering symmetrical and asymmetrical cases. Because of this, the application of this matrix has been analyzed considering untransposed three-phase transmission lines. In most of these cases, the errors related to the eigenvalues can be considered negligible. It is not true when it is analyzed the elements that are not in main diagonal of the quasi-mode matrix. This matrix is obtained from the application of Clarke's matrix. The quasi-mode matrix is correspondent to the eigenvalue matrix. Their off-diagonal elements represent couplings among the quasi-modes. So, the off-diagonal quasi-mode element relative values are not negligible when compared to the eigenvalues that correspond to the coupled quasi-modes. Minimizing these relative values, the correction procedure is analyzed in detail, checking some alternatives for the correction procedure application.

Computational Aspects of the Calculation of Isometry Groups in General Relativity

We describe the ideas behind the package 'isometry', implemented in Maple to calculate isometry groups of dimensions 2, 3 and 4 in General Relativity. The package extends the functionality of previous programs written to perform invariant classification of space-times in General Relativity. Programming solutions used to surmount problems encountered with the calculation of eigenvectors and the determination of the signs of expressions are described. We also show how the package can be used to find the Killing vectors of a space-time.

Nonmodal energetics of resistive drift waves

The modal and nonmodal linear properties of the Hasegawa-Wakatani system are examined. This linear model for plasma drift waves is nonnormal in the sense of not having a complete set of orthogonal eigenvectors. A consequence of nonnormality is that finite-time nonmodal growth rates can be larger than modal growth rates. In this system, the nonmodal time-dependent behavior depends strongly on the adiabatic parameter and the time scale of interest. For small values of the adiabatic parameter and short time scales, the nonmodal growth rates, wave number, and phase shifts (between the density and potential fluctuations) are time dependent and differ from those obtained by normal mode analysis. On a given time scale, when the adiabatic parameter is less than a critical value, the drift waves are dominated by nonmodal effects while for values of the adiabatic parameter greater than the critical value, the behavior is that given by normal mode analysis. The critical adiabatic parameter decreases with time and modal behavior eventually dominates. The nonmodal linear properties of the Hasegawa-Wakatani system may help to explain features of the full system previously attributed to nonlinearity.

Nonmodal energetics of electromagnetic drift waves

The linear properties of an electromagnetic drift-wave model are examined. The linear system is non-normal in that its eigenvectors are not orthogonal with respect to the energy inner product. The non-normality of the linear evolution operator can lead to enhanced finite-time growth rates compared to modal growth rates. Previous work with an electrostatic drift-wave model found that nonmodal behavior is important in the hydrodynamic limit. Here, similar behavior is seen in the hydrodynamic regime even with the addition of magnetic fluctuations. However, unlike the results for the electrostatic drift-wave model, nonmodal behavior is also important in the adiabatic regime with moderate to strong magnetic fluctuations. © 2000 American Institute of Physics.

An alternative procedure to decrease the dimension of the frequency dependent modal transformation matrices: Application in three-phase transmission lines with a vertical symmetry plane

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into Quasi-modes α, β and zero. After that, Quasi-modes α and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km. © 2006 IEEE.

Representation of transmission lines in modal domain using analytical transformation matrices

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which does not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show the modal transformation matrix of a hypothetical two-phase obtained with numerical and analytical procedures. It will be shown currents and voltage s at terminals of the line taking into account the use of modal transformation matrices obtained by using numerical and analytical procedures. © 2011 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model. © 2012 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model © 2003-2012 IEEE.

Estimates of genetic parameters and eigenvector indices for milk production of Holstein cows

The objectives of the present study were to estimate genetic parameters of monthly test-day milk yield (TDMY) of the first lactation of Brazilian Holstein cows using random regression (RR), and to compare the genetic gains for milk production and persistency, derived from RR models, using eigenvector indices and selection indices that did not consider eigenvectors. The data set contained monthly TDMY of 3,543 first lactations of Brazilian Holstein cows calving between 1994 and 2011. The RR model included the fixed effect of the contemporary group (herd-month-year of test days), the covariate calving age (linear and quadratic effects), and a fourth-order regression on Legendre orthogonal polynomials of days in milk (DIM) to model the population-based mean curve. Additive genetic and nongenetic animal effects were fit as RR with 4 classes of residual variance random effect. Eigenvector indices based on the additive genetic RR covariance matrix were used to evaluate the genetic gains of milk yield and persistency compared with the traditional selection index (selection index based on breeding values of milk yield until 305 DIM). The heritability estimates for monthly TDMY ranged from 0.12 ± 0.04 to 0.31 ± 0.04. The estimates of additive genetic and nongenetic animal effects correlation were close to 1 at adjacent monthly TDMY, with a tendency to diminish as the time between DIM classes increased. The first eigenvector was related to the increase of the genetic response of the milk yield and the second eigenvector was related to the increase of the genetic gains of the persistency but it contributed to decrease the genetic gains for total milk yield. Therefore, using this eigenvector to improve persistency will not contribute to change the shape of genetic curve pattern. If the breeding goal is to improve milk production and persistency, complete sequential eigenvector indices (selection indices composite with all eigenvectors) could be used with higher economic values for persistency. However, if the breeding goal is to improve only milk yield, the traditional selection index is indicated. © 2013 American Dairy Science Association.