Lamplighter groups, bireversible automata, and rational series over finite rings

Rachel Skipper; Benjamin Steinberg

doi:10.4171/ggd/555

Lamplighter groups, bireversible automata, and rational series over finite rings

Groups Geometry and Dynamics ◽

10.4171/ggd/555 ◽

2020 ◽

Vol 14 (2) ◽

pp. 567-589

Author(s):

Rachel Skipper ◽

Benjamin Steinberg

Keyword(s):

Finite Rings ◽

Rational Series ◽

Lamplighter Groups

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Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

Volume 4B: Dynamics, Vibration and Control ◽

10.1115/imece2013-63482 ◽

2013 ◽

Cited By ~ 1

Author(s):

Giuseppe Muscolino ◽

Roberta Santoro ◽

Alba Sofi

Keyword(s):

Sensitivity Analysis ◽

Series Expansion ◽

Neumann Series ◽

Mean Value ◽

Frame Structure ◽

Young’S Moduli ◽

Rational Series ◽

Power Spectral ◽

Stochastic Sensitivity Analysis ◽

Neumann Series Expansion

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

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Quotient rings of Noetherian module finite rings

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1994-1198452-2 ◽

1994 ◽

Vol 121 (2) ◽

pp. 335-335 ◽

Cited By ~ 2

Author(s):

A. W. Chatters ◽

C. R. Hajarnavis

Keyword(s):

Finite Rings ◽

Noetherian Module ◽

Quotient Rings

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Public-key cryptosystem based on invariants of diagonalizable groups

Groups – Complexity – Cryptology ◽

10.1515/gcc-2017-0003 ◽

2017 ◽

Vol 9 (1) ◽

Author(s):

František Marko ◽

Alexandr N. Zubkov ◽

Martin Juráš

Keyword(s):

Linear Algebra ◽

Finite Fields ◽

Number Fields ◽

Euclidean Algorithm ◽

Public Key ◽

Public Key Cryptosystem ◽

Finite Rings

AbstractWe develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).

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