Search results for "SPACE"
showing 10 items of 21658 documents
CCDC 1880603: Experimental Crystal Structure Determination
2018
Related Article: M.M. Abdou, M. Matziari, P.M. O'Neill, E. Amigues, R. Zhou, R. Wang, B.F. Ali|2018|IUCrData|3|x181662|doi:10.1107/S2414314618016620
CCDC 1825949: Experimental Crystal Structure Determination
2018
Related Article: Jacques Pliquett, Souheila Amor, Miguel Ponce-Vargas, Myriam Laly, Cindy Racoeur, Yoann Rousselin, Franck Denat, Ali Bettaïeb, Paul Fleurat-Lessard, Catherine Paul, Christine Goze, Ewen Bodio|2018|Dalton Trans.|47|11203|doi:10.1039/C8DT02364F
CCDC 1010853: Experimental Crystal Structure Determination
2014
Related Article: Linda Ta, Anton Axelsson, Joachim Bijl, Matti Haukka, Henrik Sundén|2014|Chem.-Eur.J.|20|13889|doi:10.1002/chem.201404288
CCDC 993834: Experimental Crystal Structure Determination
2014
Related Article: Inguna Goba, Baiba Turovska, Sergey Belyakov, Edvards Liepinsh|2014|J.Mol.Struct.|1074|549|doi:10.1016/j.molstruc.2014.06.044
CCDC 1831928: Experimental Crystal Structure Determination
2019
Related Article: Filip Topić, Katarina Lisac, Mihails Arhangelskis, Kari Rissanen, Dominik Cinčić, Tomislav Friščić|2019|Chem.Commun.|55|14066|doi:10.1039/C9CC06735C
On one-dimensionality of metric measure spaces
2019
In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a one-dimensional manifold (possibly with boundary). As an immediate corollary we obtain that if a metric measure space is a very strict $CD(K,N)$ -space or an essentially non-branching $MCP(K,N)$-space with some open set isometric to an interval, then it is a one-dimensional manifold. We also obtain the same conclusion for a metric measure space which has a point in which the Gromov-Hausdorff tangent is unique and isometric to the real line, and fo…
Differential of metric valued Sobolev maps
2020
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.
Mappings of finite distortion between metric measure spaces
2015
We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a ( 1 , 1 ) (1,1) -Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n n -manifolds of type A A has zero Hausdorff n n -measure.
Existence of optimal transport maps in very strict CD(K,∞) -spaces
2018
We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible lack of uniqueness of optimal plans. peerReviewed
Non-branching geodesics and optimal maps in strong CD(K,∞) -spaces
2014
We prove that in metric measure spaces where the entropy functional is Kconvex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant. peerReview…