Search results for "Pace"
showing 10 items of 21903 documents
CCDC 973532: Experimental Crystal Structure Determination
2014
Related Article: Ludovico G. Tulli, Negar Moridi, Wenjie Wang, Kaisa Helttunen, Markus Neuburger, David Vaknin, Wolfgang Meier, Patrick Shahgaldian|2014|Chem.Commun.|50|3938|doi:10.1039/C4CC00928B
Space-filling vs. Luzin's condition (N)
2013
Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the first space has sigma-finite measure with respect to the Hausdorff measure of the corresponding dimension. We show for quite general metric spaces that for any measurable surjection from the first onto the second space, there is a set of measure zero that is mapped to a set of positive measure (both measures are the Hausdorff measures corresponding to the Hausdorff dimension of the first space). We also study more general situations where the measures on the two metric spaces are not necessarily the same and not ne…
Visible parts of fractal percolation
2009
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.
The richest superclusters : I Morphology
2007
We study the morphology of the richest superclusters from the catalogues of superclusters of galaxies in the 2dF Galaxy Redshift Survey and compare the morphology of real superclusters with model superclusters in the Millennium Simulation. We use Minkowski functionals and shapefinders to quantify the morphology of superclusters: their sizes, shapes, and clumpiness. We generate empirical models of simple geometry to understand which morphologies correspond to the supercluster shapefinders. We show that rich superclusters have elongated, filamentary shapes with high-density clumps in their core regions. The clumpiness of superclusters is determined using the fourth Minkowski functional $V_3$.…
Multi-scale morphology of the galaxy distribution
2006
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we first show how to calculate the Minkowski Functionals (MF) taking into account these border effects. Then we present a multiscale extension of the MF which gives us more information about how the galaxies are spatially distributed. A range of examples using Gaussian random fields illustrate the results. Finally we have applied the Multiscale Minkowski Functionals (MMF) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morpho…
CCDC 784160: Experimental Crystal Structure Determination
2011
Related Article: R.Francke, G.Schnakenburg, S.R.Waldvogel|2010|Org.Lett.|12|4288|doi:10.1021/ol101698a
CCDC 1908608: Experimental Crystal Structure Determination
2019
Related Article: Clève D. Mboyi, Delphine Vivier, Ahmad Daher, Paul Fleurat-Lessard, Hélène Cattey, Charles H. Devillers, Claire Bernhard, Franck Denat, Julien Roger, Jean-Cyrille Hierso|2020|Angew.Chem.,Int.Ed.|59|1149|doi:10.1002/anie.201911947
CCDC 962106: Experimental Crystal Structure Determination
2017
Related Article: B. Elsler, D. Schollmeyer, S. R. Waldvogel|2014|Faraday Discuss.|172|413|doi:10.1039/C4FD00049H
CCDC 956780: Experimental Crystal Structure Determination
2013
Related Article: M. Lahtinen, K. Nättinen and S. Nummelin|2013|Acta Crystallogr.,Sect.E:Struct.Rep.Online|69|o810|doi:10.1107/S1600536813010969
CCDC 935635: Experimental Crystal Structure Determination
2013
Related Article: M.Lahtinen,K.Nattinen,S.Nummelin|2013|Acta Crystallogr.,Sect.E:Struct.Rep.Online|69|o510|doi:10.1107/S1600536813006053