Results 221 to 230 of about 520,811 (261)
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The Distribution of Primitive Roots
Canadian Journal of Mathematics, 1969Notation,p and q are generic symbols for prime numbers. N(H, p) denotes the number of primes q, not exceeding Hy which are primitive roots (mod p).g(p) denotes the least positive primitive root (mod p).g*(p) is the least prime primitive root (mod p).v(m) denotes the number of distinct prime divisors of the integer m.τk(m) is the number of ways of ...
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The Fractional Unit Root Distribution
Econometrica, 1990Asymptotic distributions are derived for the ordinary least squares estimate of a first order autoregression model when the series is fractionally integrated. The fractional unit root distribution is introduced to describe the limiting distribution.
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Root Barriers affect Root Distribution
Arboriculture & Urban Forestry, 1996No 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 polynomial root distribution with respect to a sector
2021 25th International Conference on Methods and Models in Automation and Robotics (MMAR), 2021This 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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On the Distribution of the Roots of Certain Symmetric Matrices
The Annals of Mathematics, 1958The 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, 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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The distribution of the root degree of a random permutation
Combinatorica, 2009Given 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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The distribution of plasmodesmata in the root tip of maize
Planta, 1969The 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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On the Limiting Distribution of Roots of a Determinantal Equation
Journal of the London Mathematical Society, 1941zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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