We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups. When Atiyah introduced L-Betti numbers for compact manifolds (later generalized to finite CW-complexes), he asked [1, p. 72] about the possible values these can assume. In...

la mer caspienne est un bassin isole de type lacustre. son regime sale depend de l'influence de l'eau douce et de l'evaporation de la nappe d'eau. la masse principale des sels vient des bassins qui occupaient son auge au pliocene et au pleistocene. cependant, des la fin du pliocene (i'age apcheron), la mer caspienne formait deja un bassin d'eau saumatre. au cours d...

Using the Modified Picard Method of Parker and Sochacki [1, 2], we derive a hybrid scheme using the analytical Picard method with approximations to the differential operators. This new method, called Discretized Picard’s Method, uses approximations in the space dimensions to compute derivatives but utilizes a continuous approximation in the time dimension. We illustrate the method using finite ...

In the sequel, we shall denote the single-valued normalized duality map by j. Let F (T ) = {x ∈ E : Tx = x} denote the set of all fixed point for a mapping T . We write xn ⇀ x (respectively xn ∗ ⇀ x) to indicate that the sequence xn weakly (respectively weak∗) converges to x; as usual xn → x will symbolize strong convergence. A mapping A : D(A) ⊂ E → 2 is called to be accretive if for all x, y ...

We study the complexity of (approximate) winner determination under the Monroe and Chamberlin–Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions (the utilitarian case) or as the (dis)satisfactio...