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Canadian Journal of Mathematics, 1987
A great part of mathematical analysis relies directly on the methods of separation of variables and on the successive reduction of several variables problems to one-dimensional equations and to the theory of classical special functions; for example, the theory of elliptic or parabolic equations with regular coefficients (even with non constant ...
Debiard, Amédée, Gaveau, Bernard
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A great part of mathematical analysis relies directly on the methods of separation of variables and on the successive reduction of several variables problems to one-dimensional equations and to the theory of classical special functions; for example, the theory of elliptic or parabolic equations with regular coefficients (even with non constant ...
Debiard, Amédée, Gaveau, Bernard
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Root and Root System Terminology
Forest Science, 1983Abstract This dictionary of more than 2,200 terms relating to roots and root systems is biased toward forestry but will also be useful to workers in plant anatomy, morphology, ecology, nutrition, pathology, physiology, and propagation. It attempts to be exhaustive in English and also includes many foreign terms.
R. F. Sutton, R. W. Tinus
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Root system architecture : from individual roots to root systems
2011International ...
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2004
A Euclidean space is a real vector space \(\mathcal{V}\) endowed with an inner product, that is, a positive definite symmetric bilinear form. We denote this inner product by \(\left \langle \;,\;\right \rangle\). If \(0\neq \alpha \in \mathcal{V}\), consider the transformation \(s_{\alpha }: \mathcal{V}\longrightarrow \mathcal{V}\) given by ...
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A Euclidean space is a real vector space \(\mathcal{V}\) endowed with an inner product, that is, a positive definite symmetric bilinear form. We denote this inner product by \(\left \langle \;,\;\right \rangle\). If \(0\neq \alpha \in \mathcal{V}\), consider the transformation \(s_{\alpha }: \mathcal{V}\longrightarrow \mathcal{V}\) given by ...
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Root Polytopes of Crystallographic Root Systems
2015Let \(\Phi\) be a finite (reduced) irreducible crystallographic root system. We give a case-free explicit description of the convex hull of all roots in \(\Phi\), that we denote by \(\mathcal{P}_{\Phi }\) and call the root polytope of \(\Phi\). This description is attained by considering a set of distinguished faces, indexed by the subsets of a fixed ...
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Understanding the Intricate Web of Phytohormone Signalling in Modulating Root System Architecture
International Journal of Molecular Sciences, 2021Manvi Sharma +2 more
exaly