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A note on certain ergodicity coeflcients

100%
Tudisco F.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector problem Ax = x as a particular M-matrix linear system, whose coefficient matrix can be defined in terms of the entries of A. Such property turns out to generalize the two known equivalent formulations of the Pagerank centrality of a graph.
2
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Feedback equivalence of convolutional codes over finite rings

84%
DeCastro-García N.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1495-1508
EN
The approach to convolutional codes from the linear systems point of view provides us with effective tools in order to construct convolutional codes with adequate properties that let us use them in many applications. In this work, we have generalized feedback equivalence between families of convolutional codes and linear systems over certain rings, and we show that every locally Brunovsky linear system may be considered as a representation of a code under feedback convolutional equivalence.
3
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Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

68%
Koksal M. E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
693-704
EN
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.
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