Results 271 to 280 of about 6,155,597 (302)
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On the distribution of roots of polynomials in sectors. II
Lithuanian Mathematical Journal, 1998Let \(P(X)=a_nX^n+\cdots+a_0\) (\(a_0,a_n\neq 0\)) be a complex polynomial. For \(0\leq\psi\leq\varphi\leq 2\pi\) denote by \(N_P(\psi,\varphi)\) the number of roots \(z\) of \(P\) satisfying \(\psi\leq\arg z\leq\varphi\), and put \[ E_P=E_P(\psi,\varphi)=\biggl| N_P(\psi,\varphi)-{(\psi-\varphi)n\over 2\pi} \biggr|. \] It was shown by \textit{P. Erdős}
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On A Root Distribution Criterion For Interval Polynomials
Singapore International Conference on Intelligent Control and Instrumentation [Proceedings 1992], 1992H. Kokame and T. Mori (1991) and C.B. Soh (1990) derived conditions under which an interval polynomial has a given number of roots in the open left-half plane and the other roots in the open right-half plane. However, the one-shot-test approach using Sylvester's resultant matrices and Bezoutian matrices implies that the implemented conditions are only ...
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On the distribution of primitive roots modulo $p$
Publicationes Mathematicae Debrecen, 1998Summary: Let \(p\geq 3\) be a prime. For each primitive root \(x\) modulo \(p\) with \(1\leq x\leq p-1\), it is clear that there exists one and only one primitive root \(\bar x\) modulo \(p\) with \(1\leq\bar x \leq p-1\) such that \(x\bar x\equiv 1 \bmod p\).
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Distribution and Function of Proteoid Roots and other Root Clusters
Botanica Acta, 1995Abstract Proteoid roots are bottlebrush‐like clusters of rootlets which form along lateral roots. They are characteristic of most species of the Proteaceae, which are mainly distributed in Australia and South Africa. Homologous root clusters are present in species of the Casuarinaceae, Mimosaceae, Fabaceae, Myricaceae and Moraceae ...
Barbara Dinkelaker +2 more
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On the Uniform Distribution of the Roots of Certain Polynomials
The Annals of Mathematics, 1942This is a continuation of a study of the problems considered by \textit{P. Erdős} and \textit{P. Turán} [Ann. Math. (2) 41, 162--173 (1940; Zbl 0023.02201)].
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Aircraft Engineering and Aerospace Technology, 1944
THE “escalator” method of solving frequency equations, developed by Morris and Head (Ref. 1), and the natural extension of a Lemma by Professor Temple, together enable simple proofs to be given of two important fundamental theorems:
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THE “escalator” method of solving frequency equations, developed by Morris and Head (Ref. 1), and the natural extension of a Lemma by Professor Temple, together enable simple proofs to be given of two important fundamental theorems:
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Distribution of Root Tips and Tender Roots of Beech
1971F. H. Meyer, D. Göttsche
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