We study the positive Hermitian curvature flow on space of left-invariant metrics complex Lie groups. show that in nilpotent case, exists for all times and subconverges Cheeger-Gromov sense to a soliton. also convergence soliton when group is almost abelian. That is, its algebra admits (complex) co-dimension one abelian ideal. Finally, we solitons almost-abelian setting. prove uniqueness comple...

We emulate the Rademacher functions on any non-commutative compact group requiring the resulting system to have pairwise disjoint spectra. Introduction Let G be a compact topological group with normalized Haar measure μ and dual object Ĝ. Let π : G → U(Hπ) be an irreducible unitary representation of G. Then, given an integrable function f : G → C, the Fourier coefficient of f at π is defined as...

Given a topological groupG (usually compact abelian), the authors study the poset D = D(G) of dense subgroups of G and its impact on the algebraic structure of G. A key tool for this is the subgroup den(G) := ∩ D. Definition. For a cardinal κ ≥ 1, a topological group is in the class Ff (κ) [F(κ); F2(κ); Fad(κ), respectively] if some family of κ-many dense subgroups of G is independent and freel...

Vertex betweenness centrality is essential in the analysis of social and information networks, and it quantify vertex importance in terms of its quantity of information along geodesic paths in network. Edge betweenness is similar to the vertex betweenness. Co-betweenness centrality is a natural developed notion to extend vertex betweenness centrality to sets of vertices, and pairwise co-between...