Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

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.

Change of the vortex lattice symmetry in the vicinity of the macro-to-mesoscopic threshold

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On a symmetry in strong distributions

A strong Stieltjes distribution d psi(t) is called symmetric if it satisfies the propertyt(omega) d psi(beta(2)/t) = -(beta(2)/t)(omega) d psi(t), for t is an element of (a, b) subset of or equal to (0, infinity), 2 omega is an element of Z, and beta > 0.In this article some consequences of symmetry on the moments, the orthogonal L-polynomials and the quadrature formulae associated with the distribution are given. (C) 1999 Elsevier B.V. B.V. All rights reserved.

SINGULARITY THEORY and FORCED SYMMETRY BREAKING IN EQUATIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Unconstrained variables of non-commutative open strings

The boundary conditions of the bosonic string theory in non-zero B-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the constraint surface we derive a set of coordinates of string that are unconstrained. These coordinates represent a natural framework for the quantization of the theory.

Discrete symmetries, invisible axion, and lepton number symmetry in an economic 3-3-1 model

We show that Peccei-Quinn and lepton number symmetries can be a natural outcome in a 3-3-1 model with right-handed neutrinos after imposing a Z(11)circle timesZ(2) symmetry. This symmetry is suitably accommodated in this model when we augment its spectrum by including merely one singlet scalar field. We work out the breaking of the Peccei-Quinn symmetry, yielding the axion, and study the phenomenological consequences. The main result of this work is that the solution to the strong CP problem can be implemented in a natural way, implying an invisible axion phenomenologically unconstrained, free of domain wall formation, and constituting a good candidate for the cold dark matter.

Dynamically induced spontaneous symmetry breaking in 3-3-1 models

We show that in SU(3)(C) circle times SU(3)(L) circle times U(1)(N) (3-3-1) models embedded with a singlet scalar playing the role of the axion, after imposing scale invariance, the breaking of Peccei-Quinn symmetry occurs through the one-loop effective potential for the singlet field. We, then, analyze the structure of spontaneous symmetry breaking by studying the new scalar potential for the model, and verify that electroweak symmetry breaking is tightly connected to the 3-3-1 breaking by the strong constraints among their vacuum expectation values. This offers a valuable guide to write down the correct pattern of symmetry breaking for multi-scalar theories. We also obtained that the accompanying massive pseudo-scalar, instead of acquiring mass of order of Peccei-Quinn scale as we would expect, develops a mass at a much lower scale, a consequence solely of the breaking via Coleman-Weinberg mechanism. (c) 2005 Published by Elsevier B.V.

The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector nonlinear Schrodinger equations appear as lowest-negative and second-positive flows within the extended hierarchy. This is fully analogous to the well known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the 'negative' sector of the sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.

Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Closing the SU(3)(L)circle times U(1)(X) symmetry at the electroweak scale

We show that some models with SU(3)(C)circle times SU(3)(L)circle times U(1)(X) gauge symmetry can be realized at the electroweak scale and that this is a consequence of an approximate global SU(2)(L+R) symmetry. This symmetry implies a condition among the vacuum expectation value of one of the neutral Higgs scalars, the U(1)(X)'s coupling constant, g(X), the sine of the weak mixing angle sin theta(W), and the mass of the W boson, M-W. In the limit in which this symmetry is valid it avoids the tree level mixing of the Z boson of the standard model with the extra Z(') boson. We have verified that the oblique T parameter is within the allowed range indicating that the radiative corrections that induce such a mixing at the 1-loop level are small. We also show that a SU(3)(L+R) custodial symmetry implies that in some of the models we have to include sterile (singlets of the 3-3-1 symmetry) right-handed neutrinos with Majorana masses, since the seesaw mechanism is mandatory to obtain light active neutrinos. Moreover, the approximate SU(2)(L+R)subset of SU(3)(L+R) symmetry implies that the extra nonstandard particles of these 3-3-1 models can be considerably lighter than it had been thought before so that new physics can be really just around the corner.

On the N=2 superstring BRST operator

We show that the BRST charge for the N = 2 superstring system can be written as Q = e(-R)(phi dz/2 pi ib gamma(+)gamma(-))e(R), when b and gamma(+/-) are super-reparametrizations ghosts. This provides a trivial proof of the nilpotence of this operator. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Lorentz invariance of the pure spinor BRST cohomology for the superstring

In a previous Letter. The BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this Letter, the SO(9, 1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology. (C) 2001 Published by Elsevier B.V. B.V.