ovals of Cassini


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Related to ovals of Cassini: nephroid of Freeth

ovals of Cassini

pl n
(Mathematics) maths the locus of a point x, whose distance from two fixed points, a and b, is such that |xa| |xb| is a constant
[C18: named after G. D. Cassini]
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References in periodicals archive ?
And I for one did not know that the shape of the two pieces of leather that cover a baseball are known as the "ovals of Cassini" until the three explained that as well.
Here, we investigate the relationships between G(A), the union of Gersgorin disks, K(A), the union of Brauer ovals of Cassini, and B(A), the union of Brualdi lemniscate sets, for eigenvalue inclusions of an n x n complex matrix A.
Gersgorin disks, Brauer ovals of Cassini, Brualdi lemniscate sets, minimal Gersgorin sets.
Gersgorin Disks and Ovals of Cassini. For any n [greater than or equal to] 2, let A be any n x n complex matrix (written A = [[a.sub.i,j]] [member of] [C.sup.nxn]), and let [sigma](A) denote its spectrum (i.e., [sigma](A) := {[lambda] [member of] C : det[A - [lambda][I.sub.n]] = 0}).
In other words, for n [greater than or equal to] 3, each point of the Brauer ovals of Cassini K(A) is an eigenvalue of some matrix in (A) or [??](A), and, given only the data of (1.5), K(A) does a perfect job of estimating the spectra of all matrices in (A) or [??](A).
The coverage area of a bistatic radar is not a simple circle, as is the case with a monostatic radar, but one of a series of curves referred to as the Ovals of Cassini. The curves are the loci of points whose distances from the foci (receiver and transmitter) are a constant equal to the product of the distance R, and R[.sub.2] (see Figure 1).
Equation 10 defines the coverage area of a bistatic radar which is represented by one of the curves within the Ovals of Cassini.