Publications related to Confocal conic sections

HYPERBOLA METHOD ON TORIC VARIETIES

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Ecole Polytechnique2024

Cloaking property of a plasmonic structure in doubly complementary media and three-sphere inequalities with partial data

Hoài-Minh Nguyên

We investigate cloaking property of negative-index metamaterials in the time-harmonic electromagnetic setting for the so-called doubly complementary media. These are media consisting of negative-index metamaterials in a shell (plasmonic structure) and posi ...

2020

Splitting fields of conics and sums of squares of rational functions

David Maximilian Grimm

Given a geometrically unirational variety over an infinite base field, we show that every finite separable extension of the base field that splits the variety is the residue field of a closed point. As an application, we obtain a characterization of functi ...

Springer-Verlag2013

Snakes With an Ellipse-Reproducing Property

Michaël Unser, Philippe Thévenaz, Chandra Sekhar Seelamantula, Ricard Delgado Gonzalo

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. Whi ...

IEEE2012

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

A method to determine the onset voltage of single and arrays of electrospray emitters

Herbert Shea, Renato Krpoun

This paper reports on an accurate and rapid method to compute the onset voltage for a single or for an array of electrospray emitters with complex geometries and on the correlation of the simulation with experimental data. This method permits the exact det ...

American Institute of Physics2008

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007