Results 221 to 230 of about 212,635 (266)

Multiple idiopathic root resorption

Oral Surgery, Oral Medicine, Oral Pathology, 1970
Abstract Resorption of individual teeth is a common phenomenon, but there are few reported cases of multiple idiopathic root resorption. This article reports progressive root resorption in two female patients. The resorptive process begins in the area of the cementoenamel junction of vital teeth and progressively involves all or nearly all of the ...
D A, Kerr, R M, Courtney, E J, Burkes
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On Integer Polynomials with Multiple Roots

Mathematika, 2007
The authors prove the following result Theorem 1. Let \(P(X)\) be a polynomial of degree \(n \geq 2\). Denote by \(\alpha\) a zero of \(P\) of order \(s\) and \(\beta\) another zero of \(P\) of order \(t\geq s\), then \[ | \alpha-\beta| \geq 2^{-n/(2t)}(n+1)^{-n/(2s)-3n/(4st)}\text{H}(P)^{-n/(st)}\max\{1,| \alpha| \}\max\{1,| \beta| \}, \] where ...
Amou, Masaaki, Bugeaud, Yann
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Multiple external root resorption

The Journal of the American Dental Association, 1989
Presented is an unusual case of multiple external root resorption. Although the cause of this resorption was not determined, several possibilities are presented. Trauma from occlusion, periodontal and pulpal inflammation, and resorption of idiopathic origin are all discussed as possible causes.
W Z, Yusof, M N, Ghazali
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An excellent numerical technique for multiple roots

Mathematics and Computers in Simulation, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Janak Raj Sharma, Sunil Kumar
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ON ROOT MULTIPLICITIES OF $H A_n^{(1)}$

International Journal of Algebra and Computation, 2002
We determine the root multiplicities of the Kac–Moody Lie algebra [Formula: see text] of indefinite type using a recursive root multiplicity formula due to Kang. We view [Formula: see text] as a representation of its subalgebra [Formula: see text] and then use the combinatorics of the irreducible representations of [Formula: see text] to determine the
Jennifer Hontz, Kailash C. Misra
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An Existence Test for Root Clusters and Multiple Roots

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1988
Let f be analytic in the interior of the disk \(K(\tilde z;r)\) with center \(\tilde z\) and radius r, and let ...
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Newton's method for multiple roots

Computers & Graphics, 1994
Abstract We investigate the basins of attraction in the complex plane of Newton's method for finding multiple roots and illustrate what happens as two simple roots coalesce to form a double root.
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