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Generators, Relations and Groebner basis(Algebraic Manipulation for Differential Equations)

Generators, Relations and Groebner basis(Algebraic Manipulation for Differential Equations)
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Coupling Matrix Synthesis Using Groebner Basis

2022 24th International Microwave and Radar Conference (MIKON), 2022
This paper presents a new analytical approach for a problem of coupling matrix (CM) synthesis. The approach is based on reformulation of well-known equations representing filter scattering parameters S11 and S21 for a given coupling matrix.
Jędrzej Michalczyk, J. Michalski
semanticscholar   +2 more sources

Computing mobility condition using Groebner basis

Mechanism and Machine Theory, 2015
A mechanism is a set of rigid links interconnected together with ideal joints and featuring at least one degree of freedom. An overconstrained mechanism is mobile provided the links' dimensions fulfill a certain relation named the “mobility condition”. The dimensions are not independent from each other and the goal is to obtain this mobility condition.
J. Rameau, P. Serré
semanticscholar   +3 more sources

Groebner Basis in Geodesy and Geoinformatics

International Congress on Mathematical Software, 2014
In geodesy and geoinformatics, most problems are nonlinear in nature and often require the solution of systems of polynomial equations. Before 2002, solutions of such systems of polynomial equations, especially of higher degree remained a bottleneck, with iterative solutions being the preferred approach.
J. Awange, B. Paláncz, Robert H. Lewis
semanticscholar   +3 more sources

Computation of Time Optimal Feedback Control Using Groebner Basis

IEEE Transactions on Automatic Control, 2014
The synthesis of time optimal feedback control of a single input continuous time linear time invariant (LTI) system is considered. If the control input u(t) is constrained to obey |u(t)| ≤ 1, then it is known that the optimal input switches between the extreme values ±1, according to some “switching surfaces” in the state space.
Deepak U. Patil, D. Chakraborty
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Application of Groebner Basis Methodology to Nonlinear Mechanics Problems

International Congress on Mathematical Software, 2014
The application of the Groebner basis methodology to four nonlinear mechanics problems is discussed. The MAPLE software package is used in all cases to implement the Groebner basis calculation which converts a set of coupled polynomial algebraic equations into an equivalent set of uncoupled polynomial algebraic equations (the reduced Groebner basis ...
Y. Liu, J. Peddieson
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Information sets in abelian codes: defining sets and Groebner basis

Designs, Codes and Cryptography, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
José Joaquín Bernal, J. Simón
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Application of Groebner Basis Methodology to Nonlinear Static Cable Analysis

Journal of Offshore Mechanics and Arctic Engineering, 2013
The governing equations for large deflections of cables have a highly nonlinear and coupled nature, which precludes exact analytical solutions except in a few simplified cases. The present study demonstrates the utility of Groebner Basis methodology in facilitating the construction of approximate analytical and semianalytical Galerkin solutions in the ...
Y. Liu, G. Buchanan, J. Peddieson
semanticscholar   +2 more sources