In this paper we discuss ellipticity conditions for some parameter-dependent boundary value problems which do not satisfy the Agmon–Agranovich–Vishik condition of ellipticity with parameter. The appropriate definition of ellipticity uses the concept of the Newton polygon. For the corresponding boundary value problems with small parameter we construct the formal asymptotic solution, thus explain...

We compute both extrinsic (lensing) and intrinsic contributions to the (galaxy-)density-ellipticity correlation function, the latter done using current analytic theories of tidal alignment. The gravitational lensing contribution has two components: one is analogous to galaxy-galaxy lensing and the other arises from magnification bias – that gravitational lensing induces a modulation of the gala...

We revisit the shapes of isophotes for elliptical (E) and lenticular (S0) galaxies by studying 847 nearby early-type galaxies selected from the Sloan Digital Sky Survey Data Release 4 with velocity dispersions above 200 km s. The IRAF task ellipse was used to derive the deviations of the isophotes from pure ellipses (Fourier coefficients a3/a and a4/a), position angles and ellipticities as a fu...

We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves...

We derive new upper limits on the ellipticity of pulsars whose braking index has been measured, more tightening than those usually given, assuming that both a gravitational torque and an electromagnetic one act on them. We show that the measured braking indexes of pulsars are recovered in this model. We consider the electromagnetic torque both constant and varying with time. At the same time co...

Let S = {St}t≥0 be the submarkovian semigroup on L2(R ) generated by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients cij . Further let Ω be an open subset of R . We prove that S leaves L2(Ω) invariant if, and only if, it is invariant under the flows generated by the vector fields Yi = ∑d j=1 cij∂j .

When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf-sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf-sup condition ca...

We develop a new cosmic void finding technique based on methods of Lagrangian orbit reconstruction. We propose to define voids as the source point of repulsion of the comoving motion of galaxies in the Universe. We re-define the position and the ellipticity of voids in this Lagrangian framework. We discuss the advantage of this new void finder compared to existing Eulerian techniques. We then d...

We consider partial differential operators H = − div(C∇) in divergence form on R with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients. First, we prove that one can define H as a selfadjoint operator on L2(R ) such that the corresponding semigroup extends as a positive, contraction semigroup to all the Lp-spaces. Secondly, we establish that H is strongly elliptic if and only...

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated sym...