Search results for "Properties of polynomial roots"

showing 2 items of 2 documents

Nonlinear embeddings: Applications to analysis, fractals and polynomial root finding

2016

We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors, coefficients of a generating function...) to their ordinary sum at $\kappa \to \infty$. We show that $\mathcal{B}_{\kappa}$-embeddings can be used to design nonlinear irreversible processes through this connection. A number of examples of increasing complexity are worked out to illustrate the possibilities uncovered by this concept. These include not only smooth functions but also fractals on the real line and on the complex plane. As an application, we use $\mat…

Discrete mathematicsPolynomialGeneral MathematicsApplied MathematicsGeneral Physics and AstronomyParameterized complexityFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Pattern Formation and Solitons (nlin.PS)Nonlinear Sciences - Pattern Formation and Solitons01 natural sciencesNonlinear Sciences - Adaptation and Self-Organizing Systems010305 fluids & plasmasProperties of polynomial rootsNonlinear system0103 physical sciencesCountable setConnection (algebraic framework)010306 general physicsComplex planeReal lineAdaptation and Self-Organizing Systems (nlin.AO)Mathematical PhysicsMathematics
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On the simultaneous determination of polynomial roots

1982

CombinatoricsProperties of polynomial rootsMathematics
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