The equivalence transformation between Galois NFSRs and Fibonacci NFSRs

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Yongyi Yan ◽  
Jun‐e Feng
Keyword(s):  
Equivalence Transformation

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

Normalized Modeling of Piezoelectric Energy Harvester Based on Equivalence Transformation and Unit-Less Parameters

2019 ◽  
Vol 28 (4) ◽  
pp. 666-677 ◽  
Author(s):  
Lucas S. Mendonca ◽  
Leandro T. Martins ◽  
Matthias Radecker ◽  
Fabio E. Bisogno ◽  
Dirk Killat
Keyword(s):  
Energy Harvester ◽  
Equivalence Transformation ◽  
Piezoelectric Energy

scholarly journals The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
V. N. Grebenev ◽  
A. N. Grishkov ◽  
M. Oberlack
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Central Charge ◽  
Riemannian Metrics ◽  
Equivalence Transformation ◽  
Velocity Correlation ◽  
Correlation Tensor

The extended symmetry of the functional of length determined in an affine spaceK3of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variablet) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metricsdl2(t)(Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation spaceK3and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic formdlD22(t)generated bydl2(t)which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric formcas for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame ofdlD22(t).

scholarly journals A Method of Symmetrization of Asymmetric Dynamical Systems

2005 ◽  
Vol 12 (4) ◽  
pp. 309-315 ◽  
Author(s):  
C.Q. Liu
Keyword(s):  
Dynamical Systems ◽  
Numerical Calculations ◽  
Equivalence Transformation ◽  
Symmetric Matrices ◽  
New Approach ◽  
Symmetric Systems

This paper presents an approach to transform asymmetric systems into symmetric systems by equivalence transformation and discusses what forms of restrictions should be imposed on the system matrices so that they can be simultaneously transformed into symmetric matrices. Conditions of symmetrizability obtained here are more “liberal” and numerical calculations of this transformation are more straightforward. Several examples are provided to illustrate the new approach.

The Use of Multibody System Modeling and Multivariable System Decoupling Techniques in Vehicle Ride Control

1999 ◽  
Vol 121 (3) ◽  
pp. 479-486 ◽  
Author(s):  
A. S. Cherry ◽  
R. P. Jones ◽  
T. E. C. Potter
Keyword(s):  
Multibody System ◽  
System Modeling ◽  
Analytical Techniques ◽  
Equivalence Transformation ◽  
Single Input Single Output ◽  
Single Output ◽  
Modal Damping ◽  
Ride Control ◽  
Single Input ◽  
Siso Systems

This paper describes the use of realistic analytical techniques to address automotive ride control. Multibody system (MBS) modeling techniques were used to develop a full vehicle model with suspension system representation, which was subsequently validated against experimental data. The resultant multivariable ride control problem was then decoupled in the frequency domain by the application of equivalence transformation techniques. It is shown that diagonalization can be achieved for the range of primary ride frequencies, and that the decoupled system then consists of three single-input/single-output (SISO) systems, one for each of the sprung mass modes. Finally, feedback control design for each sprung mass mode loop is illustrated by the application of modal damping.

scholarly journals Reduction of Linear Functional Systems using Fuhrmann's Equivalence

2016 ◽  
Vol 21 (1) ◽  
pp. 64
Author(s):  
Mohamed S. Boudellioua
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Linear Functional ◽  
Single Equation ◽  
Functional System ◽  
Equivalence Transformation ◽  
Functional Systems ◽  
Delay Differential ◽  
Number Of Authors

Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.  

Sign in / Sign up

Export Citation Format

Share Document