We adjust methods of computable model theory to effective analysis. We use index sets and infinitary logic to obtain classificationtype results for compact computable metric spaces. We show that every compact computable metric space can be uniquely described, up to an isomorphism, by a computable Π3 formula, and that orbits of elements are uniformly given by computable Π2 formulas. We show that...

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

We define a regularized version of an equivariant index of a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Our definition requires an additional data – an equivariant map v : M → g = LieG, such that the corresponding vector field on M does not vanish outside of a compact subset. For the case when M = C and G is the circle group a...

Cellular base stations (BTS) and microwave relays have detached LNA stages located up in the aerial tower in order to mitigate NF degradation from pre-LNA cable loss. In the BTS architecture, the LNA stage is preceded by a transmit-receive (Tx-Rx) diplexer for duplexing a common aerial and by an interference fi lter for preventing out-ofband blocking or desensitization. However, both duplexer a...

Let Γ be a finitely generated group having the property that any action of any finite-index subgroup of Γ by homeomorphisms of the circle must have a finite orbit. (By a theorem of É. Ghys, lattices in simple Lie groups of real rank at least 2 have this property.) Suppose that such a Γ acts on a compact manifold M by automorphisms of a codimension-one C foliation, F . We show that if F has a co...

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds whose co-index of symmetry is less or equal than three. We will also construct many examples which arise from the theory of polars and centrioles in Riemannia...

The torsion index is a positive integer associated by Grothendieck to any connected compact Lie group G [10]. Knowing the torsion index of a group has direct consequences for the integral cohomology of the classifying space BG, the complex cobordism of BG, the Chow ring of BG, and the classification of G-torsors over fields. These applications of the torsion index are summarized in my paper [25...