Dimensional regularization is applied to the computation of the gravitational wave field generated by compact binaries at the third post-Newtonian (3PN) approximation. We generalize the wave generation formalism from isolated post-Newtonian matter systems to d spatial dimensions, and apply it to point masses (without spins), modelled by delta-function singularities. We find that the quadrupole ...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

Therefore, the potential V is subquadratic and the operator − ε 2 ∆q+V (q) is essentially self–adjoint on the Schwartz space. Such systems naturally arise in quantum chemistry when studying the dynamics of large molecules in the frame of Born-Oppenheimer approximation. The parameter ε is small because it encounters for the ratio of the mass of the electron and of the averaged mass of the nuclei...

In this paper, we are concerned with the derivation of a local error representation for exponential operator splitting methods when applied to evolutionary problems that involve critical parameters. Employing an abstract formulation of differential equations on function spaces, our framework includes Schrödinger equations in the semi-classical regime as well as parabolic initial-boundary value ...

Abstract We consider functionals given by the sum of perimeter and double integral some kernel g : ℝ N × → + {g:\mathbb{R}^{N}\times\mathbb{R}^{N}\to\mathbb{R}^{+}} , multiplied a “mass parameter” ε. show...

CP violation in the neutral kaon system is known to be dominated by the mixing of K 0 and K 0. Direct CP violation in the 2 pion decays of neutral kaons has been a controversial subject over the last decade. A strong experimental effort has been devoted to the precise measurement of the direct CP violation parameter ℜe (ε ′ /ε). After 10 years of detector development, data collection and analys...

The aim of this paper is to extend the analysis of Cuckoo Hashing of Devroye and Morin in 2003. In particular we make several asymptotic results much more precise. We show, that the probability that the construction of a hash table succeeds, is asymptotically 1 − c(ε)/m + O(1/m) for some explicit c(ε), where m denotes the size of each of the two tables, n = m(1 − ε) is the number of keys and ε ...

In this paper we present a rigorous derivation of the effective model for enhanced diffusion through a narrow and long 2D pore. The analysis uses a singular perturbation technique. The starting point is a local pore scale model describing the transport by convection and diffusion of a reactive solute. The solute particles undergo a first-order reaction at the pore surface. The transport and rea...