<p style='text-indent:20px;'>We consider certain elliptical subsets of the square lattice. The recurrent representative identity element sandpile group on this graph consists predominantly a biperiodic pattern, along with some noise. We show that as lattice spacing tends to 0, fraction area taken up by pattern in 1.</p>

Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g. computer graphics [1], coordinate metrology [2], petroleum engineering [11], statistics [7]. In the past, algorithms have been given which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points [1], [6]. In this paper we p...

The k-ellipse is the plane algebraic curve consisting of all points whose sum of distances from k given points is a fixed number. The polynomial equation defining the k-ellipse has degree 2k if k is odd and degree 2k− ` k k/2 ́ if k is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted k-ellipses and k-...

This paper considers the fitting of ellipses to edge-based pixel data in digital images. It infers the ellipses as projected circles, viewed obliquely, and uses this information to constrain the position, viewpoint and scale of model objects projected onto the image. A central theme of the work is the explicit use of uncertainty, which reflects observation errors in the image data, and which is...

A method is proposed for determining the number of damaged stator windings in presence an asymmetric power supply system induction electric motor based on Park vector hodograph. As a result experiments simulation model, it was found that with symmetry voltages and windings, hodograph describes circle; all other cases ellipse. It has been established asymmetry voltage indicated by angle inclinat...