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Cluster roots: some ecological considerations
Journal of Ecology, 1998It has been said that the 'roots of ecology are in the ecology of roots' (Sen 1980). The study of resource acquisition by roots is a vibrant and challenging field today, and an important meeting point between ecology, physiology and developmental biology. Most of the essential elements for all life forms enter the biosphere through the roots of plants,
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Maize and soybean root clustering as indicated by root mapping
Plant and Soil, 1991Horizontal and vertical root mapping was used to relate rooting to a structured soil environment. Selected horizontal planes and associated vertical walls were exposed, and root locations were marked on polyethylene sheets. Separate sheets were used to indicate pores and cracks.
S. D. Logsdon, R. R. Allmaras
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Stability, Root Clustering and Inners
IFAC Proceedings Volumes, 1972Abstract In this paper, the recently introduced approach of Inners to some problems of system theory is further extended to stability, relative stability and aperiodicity conditions for both linear time-invariant continuous and discrete systems. It is shown that by the introduction of the Inners approach a unified theoretical and computational ...
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Linear matrix equations and root clustering
International Journal of Control, 1989Abstract Given A e ℂn + n and ϰ ⊂ ℂ, we search for a criterion assuring that the spectrum of A is clustered in ϰ, σ(A)⊂ ϰ One approach to root clustering is the linear matrix equation, whose half plane version dates back to Lyapunov. The existing literature deals with an algebraic region defined by a single polynomial.
SHAUL GUTMAN, HEDI TAUB
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Root clustering for rational convex regions
Journal of the Franklin Institute, 1984The root clustering problem is to find necessary and sufficient conditions for the spectrum of a given real matrix A to lie in some algebraic region. This paper is focused on root clustering (exclusion) with respect to rational convex regions. For root clustering the region is constructed as an intersection of infinite number of half planes, and for ...
Gutman, Shaul, Chojnowski, Fabian
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Computing clustered close-roots of univariate polynomials
Proceedings of the 2009 conference on Symbolic numeric computation, 2009Given a univariate polynomial having well-separated clusters of close roots, we give a method of computing close roots in a cluster simultaneously, without computing other roots. We first determine the position and the size of the cluster, as well as the number of close roots contained.
Tateaki Sasaki, Akira Terui
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A test for root-clustering transformability
IEEE Transactions on Automatic Control, 1982Consider the problem of root clustering: given a square matrix A with spectrum \sigma(A) , for what region S in the complex plane is it possible to state a criterion (necessary and sufficient conditions) so that \sigma(A) \in S ? Recently it has been shown that one subclass Ω of S satisfies a certain transformability condition.
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Matrix root clustering in algebraic regions
International Journal of Control, 1984Transformable regions are those which admit a root clustering criterion. In this paper we extend the notion of transformability, present root clustering criteria, and point out a future direction for investigation.
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Root Clustering in Parameter Space
1990Review of classical results.- to root clustering.- Transformable regions.- Root clustering criteria.- Symmetric matrix approach.- Parameter space and feedback design.
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