........................................................................................................................................................ 2 Acknowledgements ....................................................................................................................................... 3 Introduction .............................................................................

The subject under discussion in this paper is the study of the existence and properties of extensions of homeomorphisms of the interior I of a two cell with boundary C onto a plane bounded region. Particular emphasis will be placed on the action of the extension on C. Application of the topological results will then be made to conformai maps on the interior of the unit circle. The hypothesis th...

We consider a totally asynchronous stochastic approximation algorithm, Q-learning, for solving finite space stochastic shortest path (SSP) problems, which are total cost Markov decision processes with an absorbing and cost-free state. For the most commonly used SSP models, existing convergence proofs assume that the sequence of Q-learning iterates is bounded with probability one, or some other ...

A conservative irrational pseudo-rotation of the two-torus is semi-conjugate to the irrational rotation if and only if it has the property of bounded mean motion [1]. (Here ‘irrational pseudo-rotation’ means a toral homeomorphism with a unique and totally irrational rotation vector.) The aim of this note is to explore this concept some further. For instance, we provide an example which shows th...

Let $$M=G/K$$ be a Hermitian symmetric space of noncompact type. We provide way constructing K-equivariant embeddings from M to its tangent $$T_oM$$ at the origin by using polarity K-action. As an application, we reconstruct holomorphic embedding so called Harish-Chandra realization and symplectomorphism constructed Di Scala-Loi Roos under appropriate identifications spaces. Moreover, character...

The contact number of a packing finitely many balls in Euclidean d-space is the touching pairs packing. A prominent subfamily sphere packings formed by so-called totally separable packings: here, called if any two can be separated hyperplane such that it disjoint from interior each ball Bezdek et al. (Discrete Math. 339(2) (2016), 668–676) upper bounded numbers n unit terms and d. In this paper...

Given a prime p, number field $${K}$$ and finite set of places S , let $${K}_S$$ be the maximal pro-p extension unramified outside S. Using Golod–Shafarevich criterion one can often show that $${K}_S/{K}$$ is infinite. In both tame wild cases we construct infinite subextensions with bounded ramification using refined criterion. setting are able to produce asymptotically good extensions in which...

Let \((X, d)\) be a semimetric space and let \(G\) graph. We say that is the diametrical graph of if \(X\) vertex set adjacency vertices \(x\) \(y\) equivalent to equality \(\diam X = d(x, y)\). It shown with diameter \(d^*\) ultrametric iff d_{\varepsilon})\) \(d_{\varepsilon}(x, y) \min\{d(x, y), \varepsilon\}\) complete multipartite for every \(\varepsilon \in (0, d^*)\). A refinement last r...