This paper is an axiomatic study of consistent approval-based multi-winner rules, i.e., voting rules that select a fixed-size group of candidates based on approval ballots. We introduce the class of counting rules, provide an axiomatic characterization of this class and, in particular, show that counting rules are consistent. Building upon this result, we axiomatically characterize three import...

Abstract A general appearance of two-pole structures is exhibited in a relativistic Friedrichs–Lee model combined with quark pair creation consistent manner. This kind structure could be found when $$q\bar{q}$$ q ¯ state couples to the open-flav...

Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs. Applied in the case when the meshes are rectangle, those methods lead for example to the successfully used box scheme for the heat equation or D.S.N. scheme for the neutron transport equation. Generalizations of these methods are described ...

We employ a new second-order extension of the Lax±Friedrichs scheme, with incompressibility imposed by means of a projection algorithm, to follow the evolution of the vorticity and stress fields for a Maxwell fluid in a two-dimensional periodic system initialized with two thin and concentrated shear layers. The scheme is simple, efficient, and robust, and is capable, in particular, of resolving...

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous emission process f...

A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of order m. For every m > 3/2, we construct a rank 1 perturbation from the class Lip1 such that the corresponding operator has a sequence of eigenvalues converging to zero. Thus, near the singular point, there is no singular spectrum finiteness condition in terms...

A class of non-oscillatory numerical methods for solving nonlinear scalar conservation laws in one space dimension is considered. This class of methods contains the classical Lax-Friedrichs and the second order Nessyahu-Tadmor scheme. In the case of linear flux, new l2 stability results and error estimates for the methods are proved. Numerical experiments confirm that these methods are one-side...

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by c...

Citation: Engel A, Bange HW, Cunliffe M, Burrows SM, Friedrichs G, Galgani L, Herrmann H, Hertkorn N, Johnson M, Liss PS, Quinn PK, Schartau M, Soloviev A, Stolle C, Upstill-Goddard RC, van Pinxteren M and Zäncker B (2017) The Ocean’s Vital Skin: Toward an Integrated Understanding of the Sea Surface Microlayer. Front. Mar. Sci. 4:165. doi: 10.3389/fmars.2017.00165 The Ocean’s Vital Skin: Toward...

We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture. Invited paper for the special volume of Communications on Pure and Applied Mathematics for 75th Anniversary of the Courant Institute