The geometry of solutions to the higher dimensional Einstein vacuum equations presents aspects that are absent in four dimensions, one most remarkable being existence stably trapped null geodesics exterior asymptotically flat black holes. This paper investigates stable trapping phenomenon for two families holes, namely strings and rings, how this structure is responsible slow decay linear waves...

Let D be a division ring, T be a variable over D, σ be an endomorphism of D, δ be a σ-derivation on D and R = D[T ;σ, δ] the left skew polynomial ring over D. We show that the set (V alν(R), ) of σ-compatible real valuations which extend to R a fixed proper real valuation ν on D has a natural structure of parameterized complete non-metric tree, where is the partial order given by μ μ̃ if and onl...

In this paper we prove the following result. LetH be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D : A(H) → L(H) satisfying the relation D(An) = D(A)A∗n−1 + AD(An−2)A∗ + An−1D(A) for all A ∈ A(H) and some fixed integer n > 1. In this case there exists a uniqu...

We provide a generalization of pseudo-Frobenius numbers numerical semigroups to the context simplicial affine semigroups. In this way, we characterize Cohen-Macaulay type semigroup ring K[S]. define S, type(S), in terms some Apéry sets S and show that it coincides with ring, when K[S] is Cohen-Macaulay. If d-dimensional embedding dimension at most d+2, then type(S)?2. Otherwise, type(S) might b...