Search results for "FOS: Mathematics"
showing 10 items of 1448 documents
Some considerations on the nonabelian tensor square of crystallographic groups
2011
The nonabelian tensor square $G\otimes G$ of a polycyclic group $G$ is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of $G\otimes G$ by looking at that of $G$, on another hand, we study the nonabelian tensor product of pro--$p$--groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
2021
We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivat…
Harnack and Shmul'yan pre-order relations for Hilbert space contractions
2015
We study the behavior of some classes of Hilbert space contractions with respect to Harnack and Shmul'yan pre-orders and the corresponding equivalence relations. We give some conditions under which the Harnack equivalence of two given contractions is equivalent to their Shmul'yan equivalence and to the existence of an arc joining the two contractions in the class of operator-valued contractive analytic functions on the unit disc. We apply some of these results to quasi-isometries and quasi-normal contractions, as well as to partial isometries for which we show that their Harnack and Shmul'yan parts coincide. We also discuss an extension, recently considered by S.~ter~Horst [\emph{J. Operato…
Manifolds of quasiconformal mappings and the nonlinear Beltrami equation
2014
In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$. Moreover, we show that under regularity assumptions on $\mathcal{H}$, the manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function $\mathcal{H}$ uniquely.
Self-affine sets in analytic curves and algebraic surfaces
2018
We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces do not contain non-trivial self-affine sets. peerReviewed
Soft ditopological spaces
2015
We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between…
A metric characterization of Carnot groups
2013
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.
Torsors for Difference Algebraic Groups
2016
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for difference algebraic geometry and present an application to the Galois theory of differential equations depending on a discrete parameter.
The differential Galois group of the rational function field
2020
We determine the absolute differential Galois group of the field $\mathbb{C}(x)$ of rational functions: It is the free proalgebraic group on a set of cardinality $|\mathbb{C}|$. This solves a longstanding open problem posed by B.H. Matzat. For the proof we develop a new characterization of free proalgebraic groups in terms of split embedding problems, and we use patching techniques in order to solve a very general class of differential embedding problems. Our result about $\mathbb{C}(x)$ also applies to rational function fields over more general fields of coefficients.
A criterion for homeomorphism between closed Haken manifolds
2003
In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.