scholarly journals Non-linear spectrum-based analysis of rocking structures

Author(s):  
Natalia Reggiani Manzo ◽  
Michalis F. Vassiliou
Keyword(s):  
Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 143
Author(s):  
Jose Beltrán Jiménez ◽  
Tomi S. Koivisto

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.


1991 ◽  
Vol 39 (11) ◽  
pp. 1537-1540 ◽  
Author(s):  
A.B. Draganov ◽  
Y.N. Taranenko
Keyword(s):  

2016 ◽  
Vol 39 (7) ◽  
pp. 1017-1026 ◽  
Author(s):  
Jialiang Zhang ◽  
Jianfu Cao ◽  
Feng Gao

In this study, a novel fault diagnosis approach based on a non-linear spectrum feature is proposed for a multivariable non-linear system. The non-linear spectrum features are obtained using a non-linear output frequency response function (NOFRF) and kernel principal component analysis (KPCA). In order to improve the real-time performance of obtaining non-linear spectrum features, a frequency domain variable step size normalized least mean square (FVLMS) adaptive algorithm is presented to identify NOFRF. A multi-fault classifier based on the fusion of a support vector machine (SVM) is designed according to different frequency domain scales, and a fusion method by using sub-classifier classification reliability is proposed. A simulation example about a two-input–two-output non-linear system is provided to illustrate the effectiveness and performance of the proposed approach.


2000 ◽  
Vol 32 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Line Baribeau ◽  
Thomas Ransford
Keyword(s):  

2017 ◽  
Vol 21 (11) ◽  
pp. 2464-2467 ◽  
Author(s):  
Washim Uddin Mondal ◽  
Goutam Das

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

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