We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its conta...

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as M S. We discuss some closure properties of M S, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in M S. Most of the basic theory for regular measures is true just in ZF C. On the other hand...

We investigate the internal logic of a quantum computer with two qubits, in the two particular cases of non-entanglement (separable states) and maximal entanglement (Bell’s states). To this aim, we consider an internal (reversible) measurement which preserves the probabilities by mirroring the states. We then obtain logical judgements for both cases of separable and Bell’s states.

The mean field games system is a coupled pair of nonlinear partial differential equations arising in game theory, as limit the number agents tends to infinity. We prove existence and uniqueness classical solutions for time-dependent with Sobolev data. Many works literature assume additive separability Hamiltonian, well further structure such convexity monotonicity resulting components. Problems...

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite...

A structural description is given of the separable C∗-algebras that are contractible in KK-theory or E-theory. Subsequently it is shown that two separable C∗-algebras, A and B, are KK-equivalent if and only if there is a bundle of separable C∗-algebras over [0, 1] which is piecewise trivial with no more than six points of non-triviality such that the kernel of each fiber map is KK-contractible,...

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that...