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Characteristic Ratio Symmetric Polynomials and Their Root Characteristics
International Journal of Control, Automation and Systems, 2021For a real polynomial p(s) = ansn + ⋯ + a1s + a0, its characteristic ratios are defined by $${\alpha _i}: = {{a_i^2} \mathord{\left/{\vphantom {{a_i^2} {{a_{i - 1}}{a_{i + 1}}}}} \right.\kern-\nulldelimiterspace} {{a_{i - 1}}{a_{i + 1}}}}$$ for i = 1, 2, ⋯,
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Characteristics of patients with severe root resorption
Orthodontics & Craniofacial Research, 2004Structured AbstractAuthor – Sameshima GT, Sinclair PMObjectives – The purpose of this study was to compare a group of patients in whom all four maxillary incisors were resorbed at least 20% with a matched group.Materials and Methods – Retrospective, case–control.
G T, Sameshima, P M, Sinclair
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Root temperature effect on hydraulic characteristics of roots in hydroponics
IFAC Proceedings Volumes, 1991ABSTRACT Water uptake and gas exchange in cucumber roots ( Cucumis sativus L. cv Chojitsu-Ochiai) were examined in a root temperature control system of air-tightened hydroponics. The effect of root temperature on water uptake rate was found in a sigmoidal pattern: The water uptake rate was reduced at root temperatures lower than 12°C.
S. Yoshida, H. Eguchi
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Characteristic roots for donnell's equations with torsion
AIAA Journal, 1965= radius of cylindrical shell = parameter = (1 + A) = elasticity modulus = thickness = (-l)i>» = index = circumferential harmonic, a positive integer = complex-valued root = complexvalued root for zero prestress = (p/a)(e*)i" = const = lateral displacement ratio =-t0*/a = lateral displacement = axial coordinate = ax(e*) = circumferential coordinate = a
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Characteristic roots of quaternion matrices
Archiv der Mathematik, 1954In two recent publications [1], [2] it was shown that for matrices of (real) quaternion elements an eigenvalue theory can be developed similar to that for complex numbers. If A is such a matrix then quaternion elements λ and quaternion vectors x can be found such that Ax = xλ. ; © 1954 Springer. Eingegangen am 18. 9. 1953. To A. M.
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Characteristic Roots and Related Topics
1979The solutions of many problems in Applied Mathematics involve the so-called characteristic roots of a related matrix. Here we consider some of the important properties and concepts related to characteristic roots.
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The characteristic roots of the product of matrices
Proceedings of the Indian Academy of Sciences - Section A, 1956openaire +3 more sources