We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.

The selective entrapment of mutually annihilating species within a phase-changing carrier fluid is explored by both analytical and numerical means. The model takes full account of the dynamic heterogeneity which arises as a result of the coupling between hydrodynamic transport, dynamic phase-transitions and chemical reactions between the participating species, in the presence of a selective droplet interface. Special attention is paid to the dynamic symmetry breaking between the mass of the two species entrapped within the expanding droplet as a function of time.

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the error behaviour in the numerical dynamic.

Two conflicting high-level goals govern the enforcement of security policies, abridged in the phrase ``high security at a low cost''. While these drivers seem irreconcilable, formal modelling languages and automated verification techniques can facilitate the task of finding the right balance. We propose a modelling language and a framework in which security checks can be relaxed or strengthened to save resources or increase protection, on the basis of trust relationships among communicating parties.

Parties of reputation systems rate each other and use ratings to compute reputation scores that drive their interactions. When deciding which reputation model to deploy in a network environment, it is important to find the most suitable model and to determine its right initial configuration. This calls for an engineering approach for describing, implementing and evaluating reputation systems while taking into account specific aspects of both the reputation systems and the networked environment where they will run.

The relevant role of freight lorry parking facilities as a tool to reduce nuisances and impact of economic activities in densely populated urban areas is widely recognised in the literature. Nevertheless, the literature currently lacks specific contributions addressing the use of a complex Multiple Criteria Decision Analysis (MCDA) approach for coping with an optimal location of freight lorry parking facilities in the urban context.

This paper describes the efforts, pitfalls, and successes of applying unsupervised classification techniques to analyze the Trap-2017 dataset. Guided by the informative perspective on the nature of the dataset obtained through a set of specifically-written perl/bash scripts, we devised an automated clustering tool implemented in python upon openly-available scientific libraries. By applying our tool on the original raw data it is possibile to infer a set of trending behaviors for vehicles travelling over a route, yielding an instrument to classify both routes and plates.

In this paper we describe how to swap two 2 × 2 blocks in a real Schur form and a generalized real Schur form. We pay special attention to the numerical stability of the method. We also illustrate the stability of our approach by a series of numerical tests.