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Nobuo SATO, "A Theory for Sub-Linear Systems" in IEICE TRANSACTIONS on transactions,
vol. E68-E, no. 4, pp. 219-226, April 1985, doi: .
Abstract: Sub-linear system" is a name proposed for the systems which are non-linear in the usual addition rule but can be brought to be linear by some modification of the addition rule. The purpose of this paper is to provide a theory for a special kind of sub-linear systems in which the modified addition rule is u1u2(u1+u2)/(1u1u2) instead of u1u2. Such sub-linear systems are found to be saturable systems obtainable through mapping by hyperbolic tangent function from linear systems. They can be treated as exactly and explicitly with the mathematics remaining tractable as the corresponding linear systems, so that our accumulated knowledge on linear systems may successfully be applied to them. The sub-linear systems, however, are the systems quite different from the linear systems. The latter suffer from unavoidable or unexpected saturation or overflow of the actual hardware, but the former can be specially synthesized to take advantage of their saturating characteristic. The present theory treats the sub-linear systems with lumped constants, distributed constants, scalar fields and vector fields. And the proposed theory is expected to be applied in circuits, automatic control, communication, instrumentation, magnetics, non-linear optics, high energy-density engineering etc.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e68-e_4_219/_p
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@ARTICLE{e68-e_4_219,
author={Nobuo SATO, },
journal={IEICE TRANSACTIONS on transactions},
title={A Theory for Sub-Linear Systems},
year={1985},
volume={E68-E},
number={4},
pages={219-226},
abstract={Sub-linear system" is a name proposed for the systems which are non-linear in the usual addition rule but can be brought to be linear by some modification of the addition rule. The purpose of this paper is to provide a theory for a special kind of sub-linear systems in which the modified addition rule is u1u2(u1+u2)/(1u1u2) instead of u1u2. Such sub-linear systems are found to be saturable systems obtainable through mapping by hyperbolic tangent function from linear systems. They can be treated as exactly and explicitly with the mathematics remaining tractable as the corresponding linear systems, so that our accumulated knowledge on linear systems may successfully be applied to them. The sub-linear systems, however, are the systems quite different from the linear systems. The latter suffer from unavoidable or unexpected saturation or overflow of the actual hardware, but the former can be specially synthesized to take advantage of their saturating characteristic. The present theory treats the sub-linear systems with lumped constants, distributed constants, scalar fields and vector fields. And the proposed theory is expected to be applied in circuits, automatic control, communication, instrumentation, magnetics, non-linear optics, high energy-density engineering etc.},
keywords={},
doi={},
ISSN={},
month={April},}
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TY - JOUR
TI - A Theory for Sub-Linear Systems
T2 - IEICE TRANSACTIONS on transactions
SP - 219
EP - 226
AU - Nobuo SATO
PY - 1985
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E68-E
IS - 4
JA - IEICE TRANSACTIONS on transactions
Y1 - April 1985
AB - Sub-linear system" is a name proposed for the systems which are non-linear in the usual addition rule but can be brought to be linear by some modification of the addition rule. The purpose of this paper is to provide a theory for a special kind of sub-linear systems in which the modified addition rule is u1u2(u1+u2)/(1u1u2) instead of u1u2. Such sub-linear systems are found to be saturable systems obtainable through mapping by hyperbolic tangent function from linear systems. They can be treated as exactly and explicitly with the mathematics remaining tractable as the corresponding linear systems, so that our accumulated knowledge on linear systems may successfully be applied to them. The sub-linear systems, however, are the systems quite different from the linear systems. The latter suffer from unavoidable or unexpected saturation or overflow of the actual hardware, but the former can be specially synthesized to take advantage of their saturating characteristic. The present theory treats the sub-linear systems with lumped constants, distributed constants, scalar fields and vector fields. And the proposed theory is expected to be applied in circuits, automatic control, communication, instrumentation, magnetics, non-linear optics, high energy-density engineering etc.
ER -
English
