We consider the problem of computing a Steiner tree minimum cost under hop constraint which requires depth to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth that runs in time $n^{O(k)}$. For special case path, we give simple solves polynomial time, even if $k$ part input. The can used obtain, quasi-polynomial near-optimal solution viol...

We determine a new class of paracontact paracomplex Riemannian manifolds derived from certain cone construction, called para-Sasaki-like manifolds, and give explicit examples. define hyperbolic extension paraholomorphic manifold, which is local product two spaces equal dimension, show that it manifold. If the original manifold complete Einstein space negative scalar curvature, then its curvatur...

In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups, H⊂K⊂G, such G/K is a compact, connected, irreducible, symmetric space, and isotropy representation of G/H has exactly inequivalent, irreducible summands. We prove left metric ⟨·,·⟩t1,t2 G defined by first equation, must be an A-metric. Moreover, groups do not admit non...

The paper defines and studies new semi-Riemannian generalized Fisher metrics Fisher-like metrics, associated with entropies divergences. Examples of seven such families are provided, based on exponential PDFs. particular case when the basic entropy is a ϕ-deformed one, in sense Naudts, investigated detail, emphasis variation emergent scalar curvatures. Moreover, highlights impact these geometri...

In (Chaudhuri and Rosenfeld, 1996), metrics were developed for fuzzy sets u and v defined on the same support set S. These metrics are based on applying the Hausdorff metric to pairs of membership level sets (u 1 ( [ tk, 1 ] ), v1 ( [ tk, 1 ] ) ), where tk E [0, 1] is a (possible) membership value of u or v. The metrics of (Chaudhuri and Rosenfeld, 1996) give nice comparisons of fuzzy sets by m...