0000000000164270
AUTHOR
Michał Rams
IFS attractors and Cantor sets
Abstract We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R 3 such that every homeomorphism f of R 3 which preserves K coincides with the identity on K.
Humidity-Driven Reversible Transformation and Guest Inclusion in a Two-Dimensional Coordination Framework Tailored by Organic Polyamine Cation
Using a polyamine cation tetrenH55+ (tetren = tetraethylenepentaamine), we tailored the dynamic layered material (tetrenH5)1.6{CoII(H2O)2[MIV(CN)8]}4·xH2O (1, M = W, x = 12; 2, M = Mo, x = 11.2). 1 and 2 consist of strongly corrugated two-dimensional (2D) cyano-bridged monolayers {CoII(H2O)2[MIV(CN)8]}n2n– of square grid topology stacked in an alternate manner with cationic layers of tetrenH55+ and H2O molecules. The observed single-crystal-to-single-crystal (SCSC) transformation is due to the reversible dehydration of 1 and 2 to the respective monocrystalline materials (tetrenH5)1.6{CoII[MIV(CN)8]}4 (1deh and 2deh). Structural modifications consist of the change of coordination number (C.N…
Magneto-structural correlations in discrete $Mn^{II}‐W^V$ cyano‐bridged assemblies with polyimine ligands
We present the magneto-structural correlations for two novel discrete cyano-bridged assemblies based on cationic complexes of manganese(II) with diimine ligands and octacyanotungstate(V) ions. The crystal structure of [Mn II (terpy)(dmf)-(H 2 O) 2 ][Mn II (terpy)(H 2 O)(dmf)(μ-NC)W V (CN) 7 ] 2· 6H 2 O (1) (terpy = 2,2';6',2"-terpyridine, dmf = dimethylformamide) contains dinuclear {Mn II W V } - cyano-bridged anions, while the crystal structure of [Mn II (phen) 3 ] 2 [MnII(phen) 2 (μ-NC) 2 -W V (CN) 6 ] 2 (ClO 4 ) 2 ·9H 2 O (2) (phen = 1,10-phenanthroline) is built of tetranuclear {Mn II 2 W V 2} 2- square anions. Intramolecular Mn-W magnetic interactions through the cyano bridges are repr…
Visible parts of fractal percolation
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.
Magnetostructural correlations in CuII−NC−WV linkage: the case of [CuII(diimine)]2+−[WV(CN)8]3− 0D assemblies
International audience; We report on the syntheses, crystal structures, and magnetic properties of two cyano-bridged molecular assemblies: [CuII(phen)3]2{[CuII(phen)2]2[WV(CN)8]2}(ClO4)2·10H2O (phen = 1,10-phenanthroline) (1) and {[CuII(bpy)2]2[WV(CN)8]} {[CuII(bpy)2][WV(CN)8]}·4H2O (bpy = 2,2′-bipyridyl) (2). Compound 1 consists of cyano-bridged [CuII2WV2]2− molecular rectangles and isolated [CuII(phen)3]2+ complexes. The molecular structure of 2 reveals cyano-bridged trinuclear [CuII2WV]+ and dinuclear [CuIIWV]− ions. Magnetic interactions in 1 are interpreted in terms of the model of a tetranuclear moiety consisting of two ferromagnetic CuII−NC−WV units (J1 = +39(4) cm−1) interacting ant…