We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which arc second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it.

Some recent results on the theory of fractional Orlicz-Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter s in (0, 1) tends to either of the endpoints of its range are also discussed. This note is based on the papers [1, 2, 3, 4], where additional material and proofs can be found.

Using the new methodology introduced in a recent paper [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian level. We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics.

We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions.

We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes. (C) 2020 Elsevier B.V. All rights reserved.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, and complement those of [13], where Young functions satisfying the $\Delta_2$ and the $\nabla_2$ conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.

In this paper we provide emission estimates due to vehicular traffic via Generic Second Order Models. We generalize them to model road networks with merge and diverge junctions. The procedure consists on solving the Riemann Problem at junction assuming the maximization of the flow and a priority rule for the incoming roads. We provide some numerical results for a single-lane roundabout and we propose an application of the given procedure to estimate the production of nitrogen oxides (NOx) emission rates.

This paper describes the effect of perturbation of the kernel on the solutions of linear Volterra integral equations on time scales and proposes a new perspective for the stability analysis of numerical methods.