Results 311 to 320 of about 3,709,601 (369)

Constant solutions of polynomial equations

International Journal of Control, 1991
Abstract A necessary and sufficient condition is given for the equation AX + BY = C in polynomial matrices to have a constant solution pair X, Y and also for X to be non-singular. A sufficient condition is then established under which the equation with A and B fixed has a constant solution for each C from a given class. Applications to the construction
V. Kučera, P. Zagalák
semanticscholar   +2 more sources

Polynomial maps with constant Jacobian

Israel Journal of Mathematics, 1979
It has been long conjectured that ifn polynomialsf 1, …,f n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf 1, …,f n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically.
M. Razar
semanticscholar   +3 more sources

On polynomial controllability with polynomial state for linear constant systems

IEEE Transactions on Automatic Control, 1986
Summary: We prove that for linear, reachable, time independent dynamic systems, control at any given time may be achieved with the additional requirements that both the input and the state be polynomial functions of time. The proof is constructive and elementary, and yields a bound on the degree.
A. Ailon   +3 more
semanticscholar   +3 more sources

An Atomic Insight into the Chemical Origin and Variation of Dielectric Constant in Liquid Electrolytes.

Angewandte Chemie, 2021
Dielectric constant is a crucial physicochemical property of liquids in tuning solute-solvent interactions and solvation microstructures. Herein the dielectric constant variation of liquid electrolytes regarding to temperatures and electrolyte ...
N. Yao   +8 more
semanticscholar   +1 more source

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