In this paper, we present two variants of the Additive Schwarz Method for a Crouzeix-Raviart finite volume element (CRFVE) discretization of second order elliptic problems with discontinuous coefficients where the discontinuities are only across subd...
We prove that weakly elliptic damping gives sharp energy decay for the abstract damped wave semigroup, where the damping is not in the functional calculus. In this case, there is no overdamping. We show applications in linearised water waves and Kelv...
The stellar velocity fields of elliptical galaxies hold clues to their dynamical structure and origin. The construction of velocity field models is greatly simplified by assuming an approximate geometrical form for the streamlines of the mean stell...
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the alti...
In a recent paper, Rosen and Silverman showed that Tate's conjecture on the order of vanishing of L(E,s) implies Nagao's formula, which gives the rank of an elliptic surface in terms of a weighted average of fibral Frobenius trace values. The aim o...
Let $A_τ$ denote the elliptic associator constructed by Enriquez, a power series in two non-commutative variables $a,b$ defined as an iterated integral of the Kronecker function $F_τ$. We study a family of {\it Fay relations} satisfied by $A_τ$, d...
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image moments a...
Please note that after these results were reported at Quark Matter 2006 and posted on the preprint server it was found that what is reported here as \textit{elliptic flow fluctuations}, should rather be taken as an upper limit on the fluctuations....
as a semi-elliptical spring, elliptical spring, or cart spring, it is one of the oldest forms of vehicle suspension. A leaf spring is one or more narrow
This monograph is the core of my book "Elliptic PDEs, Measures and Capacities: From the Poisson equation to Nonlinear Thomas-Fermi Problems" which has received the 2014 EMS Monograph Award and is available in the series EMS Tracts in Mathematics publ...
Elliptical galaxies probably host the most metal rich stellar populations in the Universe. The processes leading to both the formation and the evolution of such stars are discussed by means of a new multi-zone photo-chemical evolution model, taking...
The turnover, or peak, magnitude in a galaxy's globular cluster luminosity function (GCLF) may provide a standard candle for an independent distance estimator. Here we examine the GCLF of the giant elliptical NGC 4365 using photometry of ~ 350 glob...
We show that Mochizuki's initial theta data is computable from an elliptic curve defined over $\mathbb{Q}$. We work out the case of initial theta data for the elliptic curve with Cremona label 11a1 in detail....
In this paper, we construct a family of elliptic curves with rank $\geq 5$. To do this, we use the Heron formula for a triple $(A^2, B^2, C^2)$ which are not necessarily the three sides of a triangle. It turns out that as parameters of a family of el...
Let E be an elliptic curve over Q, and let n=>1. The central object of study of this article is the division field Q(E[n]) that results by adjoining to Q the coordinates of all n-torsion points on E(Q). In particular, we classify all curves E/Q such...
Moderately large numbers of transitive elliptic spreads are constructed in characteristic $2$ and dimension $\equiv $ 2 (mod 4)....
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabu...
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only. Hence, no...
We study a two-parameter family of K3 surfaces of (generic) Picard rank $18$ which is mirror to the $18$-dimensional family of elliptically fibered K3 surfaces with a section. Members of this family are given as compactifications of hypersurfaces in...
We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces from the co...