Related papers: Problems on $\beta\mathbb{N}$
We survey some results on toric topology.
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.
We consider a bounded open subset $\Omega$ of ${\mathbb{R}}^n$ of class $C^{1,\alpha}$ for some $\alpha\in]0,1[$ and we solve the Neumann problem for the Helmholtz equation both in $\Omega$ and in the exterior of $\Omega$. We look for…
We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].
We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we…
In [Decompositions and statistics for \beta(1,0)-trees and nonseparable permutations, Advances Appl. Math. 42 (2009) 313--328] we introduced an involution, h, on \beta(1,0)-trees. We neglected, however, to prove that h indeed is an…
We will introduce a family $\Gamma_\beta, 1 < \beta \in {\mathbb{R}}$ of infinite non-amenable discrete groups as an interpolation of the Higman-Thompson groups $V_n, 1 < n \in {\mathbb{N}}$ by using the topological full groups of the…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From…
Scientometric techniques have been remarkably successful at mapping science but they face important difficulties when mapping research for societal problems possibly because they they are derived only from scientific documents and thus do…
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
We discuss quantum mechanical and topological aspects of nonabelian monopoles. Related recent results on nonabelian vortices are also mentioned.