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Your search keyword '"Exact sequence"' showing total 4 results
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4 results on '"Exact sequence"'

1. Converting high order linear PDEs to first order: Noncommutative case.

Author

Lomadze, Vakhtang

Subjects
*HIGH-order derivatives (Mathematics), *LINEAR systems, *NONCOMMUTATIVE algebras, *NUMERICAL solutions to functional equations, *MATHEMATICAL sequences
Abstract

A straightforward way is offered to convert a system of high order linear functional equations of various type into a system of first order equations. [ABSTRACT FROM AUTHOR]

Published
2017
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2. Converting high order linear PDEs to first order.

Author

Lomadze, Vakhtang

Subjects
*HIGH-order derivatives (Mathematics), *PARTIAL differential equations, *POLYNOMIALS, *COEFFICIENTS (Statistics), *NUMERICAL calculations
Abstract

A straightforward way requiring no calculations is offered to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs. [ABSTRACT FROM AUTHOR]

Published
2016
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3. Converting high order linear PDEs to first order

Author

Vakhtang Lomadze

Subjects
0209 industrial biotechnology, Constant coefficients, Exact sequence, General Computer Science, ComputingMethodologies_SIMULATIONANDMODELING, Mechanical Engineering, Mathematical analysis, MathematicsofComputing_NUMERICALANALYSIS, 0211 other engineering and technologies, 021107 urban & regional planning, 02 engineering and technology, First order, Polynomial matrix, Mathematics::Numerical Analysis, Nonlinear Sciences::Exactly Solvable and Integrable Systems, 020901 industrial engineering & automation, Control and Systems Engineering, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Applied mathematics, Electrical and Electronic Engineering, High order, Mathematics
Abstract

A straightforward way requiring no calculations is offered to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs.

Published
2016

4. A unified pole-zero module for linear transfer functions

Author

Bostwick F. Wyman and Michael K. Sain

Subjects
Exact sequence, General Computer Science, Direct sum, Mechanical Engineering, Linear system, Local ring, Free module, Field (mathematics), Rational function, Topology, Transfer function, Control and Systems Engineering, Electrical and Electronic Engineering, Mathematics
Abstract

A new module-theoretic tool is presented for the study of linear time-invariant input/output maps (‘transfer functions’). For suitable subrings 0 of the field k(s) of rational functions, an O-module called the structure module can be attached to each transfer function. This structure module naturally contains the classical (Kalman) pole module as a submodule which gives the (Wyman-Sain) multivariable zero module as the corresponding factor module. A posteriori the resulting exact sequence splits, and the structure module is isomorphic to the direct sum of the pole module and the zero module. Calculations over local rings echo valuation-theoretic results obtained by Kung and Kailath.

Published
1984

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