Sequence Covering Arrays and Linear Extensions

2015 ◽  
pp. 274-285
Author(s):  
Patrick C. Murray ◽  
Charles J. Colbourn
Keyword(s):  
Linear Extensions ◽  
Covering Arrays

Factorials Experiments, Covering Arrays, and Combinatorial Testing

2021 ◽  
Author(s):  
Raghu N. Kacker ◽  
D. Richard Kuhn ◽  
Yu Lei ◽  
Dimitris E. Simos
Keyword(s):  
Combinatorial Testing ◽  
Covering Arrays

scholarly journals Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 143
Author(s):  
Jose Beltrán Jiménez ◽  
Tomi S. Koivisto
Keyword(s):  
General Relativity ◽  
Minkowski Spacetime ◽  
Linear Extensions ◽  
Gauge Symmetries ◽  
Linear Spectrum ◽  
Massless Spin ◽  
Non Linear ◽  
Common Framework ◽  
Local Symmetries ◽  
Quadratic Action

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.

Linear extensions of dynamic systems and the reductibility problem

1970 ◽  
Vol 8 (4) ◽  
pp. 722-728
Author(s):  
S. B. Katok
Keyword(s):  
Dynamic Systems ◽  
Linear Extensions

Existence of Green-Samoilenko Functions of Some Linear Extensions of Dynamical Systems

2004 ◽  
Vol 7 (4) ◽  
pp. 454-460
Author(s):  
H. M. Kulyk ◽  
V. L. Kulyk
Keyword(s):  
Dynamical Systems ◽  
Linear Extensions

scholarly journals Linear Extensions of N-free Orders

Order ◽  
2014 ◽  
Vol 32 (2) ◽  
pp. 147-155 ◽  
Author(s):  
Stefan Felsner ◽  
Thibault Manneville
Keyword(s):  
Linear Extensions

New optimal covering arrays using an orderly algorithm

2018 ◽  
Vol 10 (01) ◽  
pp. 1850011 ◽  
Author(s):  
Idelfonso Izquierdo-Marquez ◽  
Jose Torres-Jimenez
Keyword(s):  
Small Subset ◽  
Computational Results ◽  
Covering Array ◽  
Covering Arrays ◽  
Computational Search ◽  
Minimum Number ◽  
Orderly Algorithm

A covering array [Formula: see text] is an [Formula: see text] array such that every [Formula: see text] subarray covers at least once each [Formula: see text]-tuple from [Formula: see text] symbols. For given [Formula: see text], [Formula: see text], and [Formula: see text], the minimum number of rows for which exists a CA is denoted by [Formula: see text] (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: [Formula: see text] for [Formula: see text], [Formula: see text], and [Formula: see text]. In addition, the new result [Formula: see text], and the already known existence of [Formula: see text], imply [Formula: see text].

Added Resistance in Seaways and its Impact on Yacht Performance

2007 ◽  
Author(s):  
Kai Graf ◽  
Marcus Pelz ◽  
Volker Bertram ◽  
H. Söding
Keyword(s):  
Strong Impact ◽  
Wave Spectra ◽  
Linear Extensions ◽  
Added Resistance ◽  
Optimum Length ◽  
Prediction Program ◽  
Strip Theory ◽  
Velocity Prediction ◽  
Added Resistance In Waves ◽  
Response Amplitude Operators

A method for the prediction of seakeeping behaviour of sailing yachts has been developed. It is based on linear strip theory with some non-linear extensions. The method is capable to take into account heeling and yawing yacht hulls, yacht appendages and sails. The yacht's response amplitude operators (RAO) and added resistance in waves can be predicted for harmonic waves as well as for natural wave spectra. The method is used to study added resistance in seaways for ACC-V5 yachts of varying beam. Results are used for further VPP investigations. The AVPP velocity prediction program is used to study optimum length to beam ratio of the yachts depending on wind velocity and upwind to downwind weighting. This investigation is carried out for flat water conditions as well as for two typical wave spectra. The results show that taking into account added resistance in seaways has a strong impact on predicted performance of the yacht.

scholarly journals Refining the In-Parameter-Order Strategy for Constructing Covering Arrays

2008 ◽  
Vol 113 (5) ◽  
pp. 287 ◽  
Author(s):  
Michael Forbes ◽  
Jim Lawrence ◽  
Yu Lei ◽  
Raghu N. Kacker ◽  
D. Richard Kuhn
Keyword(s):  
Covering Arrays
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