Search results for "funktio"
showing 10 items of 319 documents
Two‐dimensional metric spheres from gluing hemispheres
2022
We study metric spheres (Z,dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g:S1→S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that if (Z,dZ) is quasiconformally equivalent to S2, in the geometric sense, then g is a welding homeomorphism with conformally removable welding curves. We also show that g is bi-Lipschitz if and only if (Z,dZ) has a 1-quasiconformal parametrization whose Jacobian is comparable to the Jacobian of a quasiconformal mapping h:S2→S2. Furthermore, we show that if g−1 is absolutely continuous and g admits a homeomorphic extension with exponentially integrable distortion, then (Z,dZ) …
Sobolev homeomorphic extensions onto John domains
2020
Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous $W^{1,2}$-extension but not even a homeomorphic $W^{1,1}$-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents $p<2$. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.
Rungen lause ja sovelluksia inversio-ongelmiin
2018
Quasisymmetric extension on the real line
2015
We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to\mathbb{R}^N$ for some $N\geq n$.
Yhdesti yhtenäisten tasoalueiden konformisten itsekuvausten ryhmät sup-metriikassa
2014
Logarithmic mean inequality for generalized trigonometric and hyperbolic functions
2015
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean. peerReviewed
Harmoniset funktiot graafeilla
2017
Spatially dependent parton distribution functions and hard processes in nuclear collisions
2014
Escaping scaling relationships for water dissociation at interfacial sites of zirconia-supported Rh and Pt clusters
2019
<p>Water dissociation is an important reaction involved in many industrial processes and a good model reaction for probing the activity of catalytic sites. In this computational study, the dissociation of water at interfacial sites of globally optimized ZrO2 sup- ported Pt and Rh clusters is investigated under the framework of density functional theory. Our findings demonstrate that the perimeter sites of these small clusters can activate water, but the dissociation behavior varies considerably between sites. It is shown that the studied clusters break scaling relationships for water dissociation, suggesting these catalysts may achieve activities beyond the maximum imposed by such rel…