Results 261 to 270 of about 2,158,107 (298)

On polynomial root distribution with respect to a sector

2021 25th International Conference on Methods and Models in Automation and Robotics (MMAR), 2021
This paper extends previous results of the same authors on the determination of the polynomial root distribution with respect to a sector by means of elementary vector analysis. Specifically, it is shown how the overall phase variation of any real or complex polynomial along the radii of a sector accounts for the number of roots inside and outside the ...
Casagrande D., Krajewski W., Viaro U.
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Root Barriers affect Root Distribution

Arboriculture & Urban Forestry, 1996
No roots of live oak (Quercus virginiana) or sycamore (Platanus occidentalis) went through Biobarrier™ during a 3-year period after planting. Most roots on both species without a barrier were located in the top 30 cm (12 in) of soil, and root number decreased with increasing soil depth.
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On A Root Distribution Criterion For Interval Polynomials

Singapore International Conference on Intelligent Control and Instrumentation [Proceedings 1992], 1992
H. 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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The distribution of the root degree of a random permutation

Combinatorica, 2009
Given a permutation ω of {1, …, n}, let R(ω) be the root degree of ω, i.e. the smallest (prime) integer r such that there is a permutation σ with ω = σ r . We show that, for ω chosen uniformly at random, R(ω) = (lnlnn − 3lnlnln n + O p (1))−1 lnn, and find the limiting distribution of the remainder term.
Béla Bollobás, Boris G. Pittel
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On the Limiting Distribution of Roots of a Determinantal Equation

Journal of the London Mathematical Society, 1941
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On the distribution of primitive roots modulo $p$

Publicationes Mathematicae Debrecen, 1998
Summary: 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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The distribution of plasmodesmata in the root tip of maize

Planta, 1969
The distribution of plasmodesmata in different regions of the root apex of Zea mays has been analysed from electron micrographs. There are many more plasmodesmata traversing transverse walls than across longitudinal walls in all the regions studied. When the number of plasmodesmata per unit cell volume is calculated, cells in non-dividing tissue have a
B E, Juniper, P W, Barlow
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Symmetric and innerwise matrices for the root-clustering and root-distribution of a polynomial

Journal of the Franklin Institute, 1972
Abstract The general problem of root-clustering and root-distribution of a polynomial in a certain region Γ in the complex plane has been investigated in this paper. The region Γ is general and includes all the previously investigated regions. For the root-clustering problem, it is shown that by using a certain transformation, the necessary and ...
Jury, E. I., Ahn, S. M.
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On the Distribution of the Roots of Certain Symmetric Matrices

The Annals of Mathematics, 1958
The present article is concerned with the distribution of the latent roots (characteristic values) of certain sets of real symmetric matrices of very high dimensionality. Its purpose is to point out that the distribution law obtained before' for a very special set of matrices is valid for much more general sets.
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On the distribution of roots of polynomials in sectors. II

Lithuanian Mathematical Journal, 1998
Let \(P(X)=a_nX^n+\cdots+a_0\) (\(a_0,a_n\neq 0\)) 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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