New computational topology techniques are presented for surface reconstruction of 2-manifolds with boundary, while rigorous proofs have previously been limited to surfaces without boundary. This is done by an intermediate construction of the envelope (as defined herein) of the original surface. For any compact C manifold M embedded in R, it is shown that its envelope is C. Then it is shown that...

Given a Tonelli Hamiltonian H : T ∗M → R of class C, with k ≥ 4, we prove the following results: (1) Assume there is a critical viscosity subsolution which is of class C in an open neighborhood of a positive orbit of a recurrent point of the projected Aubry set. Then, there exists a potential V : M → R of class Ck−1, small in C topology, for which the Aubry set of the new Hamiltonian H + V is e...

This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

We consider the classes M(p)  (1 < p < ∞) of holomorphic functions on the open unit disk 𝔻 in the complex plane. These classes are in fact generalizations of the class M introduced by Kim (1986). The space M (p) equipped with the topology given by the metric ρ p defined by ρp (f, g) = ||f - g|| p = (∫0(2π) log(p) (1 + M(f - g)(θ))(dθ/2π))(1/p), with f, g ∈ M (p) and Mf(θ) = sup 0 ⩽ r<1 ⁡|f(re(i...

Let M be a convex cocompact, acylindrical hyperbolic 3-manifold of infinite volume, and let M? denote the interior core M. In this paper we show that any geodesic plane in is either closed or dense. We also only countably many planes are closed. These first rigidity theorems for cocompact 3-manifolds volume depend on topology

An intelligent strategy for the protection of AC microgrids is presented in this paper. This method was halving to an initial signal processing step and a machine learning-based forecasting step. The initial stage investigates currents and voltages with a window-based approach based on the dynamic decomposition method (DDM) and then involves the norms of the signals to the resultant DDM data. T...

Let M be a closed symplectic manifold, with symplectic form ω. A symplectic automorphism is a diffeomorphism φ : M → M such that φω = ω. We equip the group Aut(M) = Aut(M,ω) of all such maps with the C-topology. Like the whole diffeomorphism group, this is an infinite-dimensional Lie group in a very loose sense: it has a well-defined Lie algebra, which consists of closed oneforms on M , but the...

The authors discuss an approach to federated network simulations that eases the burdens on the simulation developer in creating space-parallel simulations. Previous approaches have had difficulties that arise from the need for global topology knowledge when forwarding simulated packets between federates. In all but the simplest cases, proper packet-forwarding decisions between federates require...

Generic automorphisms are a common theme when one works with auto-morphism groups of countable structures. They play a pivotal role in reconstruction results. In these notes we shall define and explain a notion of generic, due to John Truss, which is highly relevant to reconstruction. The idea is that a generic automorphism acts on the elements of the structure in the least special way, that is...

For a topological manifold M let H(M) be the group of homeomorphisms of M endowed with the Whitney topology and Hc(M) the subgroup of H(M) consisting of homeomorphisms with compact support. The identity component H0(M) of H(M) is an open normal subgroup in Hc(M) and it induces the factorization Hc(M) ≈ H0(M)×Mc(M) for the mapping class group Mc(M) = Hc(M)/H0(M). For each connected non-compact s...