We present two newly-discovered, compact elliptical (cE) galaxies, which exhibit clear evidence of tidal steams, found in a search of SDSS DR7. The structural parameters of the cEs are derived using GALFIT and give effective radii < 400 pc. They also...
We present the discovery of an isolated compact elliptical (cE) galaxy, found during a search of SDSS DR7 for cEs, and for which we obtained WHT/ACAM imaging. It is ~900 kpc distant from its nearest neighbour, has an effective r-band radius of ~500 p...
Let $(M,g)$ be a closed, smooth Riemannian manifold of dimension $m \geq 1$. It is not difficult to produce an example of a fourth order formally self-adjoint elliptic differential operator $P: C^4(M) \rightarrow C^0(M)$ that has the property that th...
This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations including Hamilton-Jacobi-Bellman equations. The proposed finite differ...
For a given elliptic curve E in short Weierstrass form, we show that almost all quadratic twists E_D have no integral points, as D ranges over square-free integers ordered by size. Our result is conditional on a weak form of the Hall-Lang conjecture...
We study whether dry merger-driven size growth of massive elliptical galaxies depends on their initial structural concentration, and analyse the validity of the homology hypothesis for virial mass determination in massive ellipticals grown by dry mer...
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryp...
In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method...
Elliptic functions are known to appear in many problems, applied and theoretical. However, a lesser known application is in the study of exact solutions to Einstein's gravitational field equations in a Friedmann-Robertson-Lemaitre-Walker (FRLW) cos...
For small odd primes $p$, we prove that most of the rational points on the modular curve $X_0(p)/w_p$ parametrize pairs of elliptic curves having infinitely many supersingular primes. This result extends the class of elliptic curves for which the i...
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as the resul...
We give a classification of rotational cmc surfaces in non-Euclidean space forms in terms of explicit parametrizations using Jacobi elliptic functions. Our method hinges on a Lie sphere geometric description of rotational linear Weingarten surfaces a...
Chemical and photometric models of elliptical galaxies with infall of primordial gas, and subsequent ejection of processed material via galactic winds, are described. Ensuring that these models are consistent with the present-day colour-luminosity...
We consider the simultaneous chemical, photometric, and gaseous thermal energy evolution of elliptical galaxies. The evolution of chemical abundances in the intracluster medium (ICM) is set by the differing timescales for gas ejection, via supernov...
Working within the classic supernovae-driven wind framework for elliptical galaxy evolution, we perform a systematic investigation into the discrepancies between the predictions of three contemporary codes -- Arimoto & Yoshii (1987, A&A, 173, 23),...
In this paper we study a nonlocal critical growth elliptic problem driven by the fractional Laplacian in presence of jumping nonlinearities. In the main results of the paper we prove the existence of a nontrivial solution for the problem under consid...
We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman's and the polynomial effective criteria of Berger, Drewitz and Ramirez originally defined for uniformly...
The elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds is computed. This is used to search for possible mirror pairs of such models. An important aspect of this work is that there is no restriction to theories for which th...
Motivated by recent work of Masser and Zannier on simultaneous torsion on the Legendre elliptic curve $E_λ$ of equation $Y^2=X(X-1)(X-λ)$, we prove that, given $n$ linearly independent points $P_1(λ), ...,P_n(λ)$ on $E_λ$ with coordinates in $\b...
A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting...