Search results for "geometry."
showing 10 items of 4386 documents
Crystal structure of bis[2,5-bis(pyridin-2-yl)-1,3,4-thiadiazole-κ2N2,N3]bis(thiocyanato-κS)copper(II)
2016
The structure of the title compound is similar to that of the related complexes [Co(C12H8N4S)2(N3)2] and [Ni(C12H8N4S)2(N3)2] in which the azide ion is substituted by the thiocyanate group. The CuN4S2 octahedron is more distorted than the CoN6 and NiN6 octahedra.
Crystal structure of a rare trigonal bipyramidal titanium(IV) coordination complex: trichlorido(3,3′-di-tert-butyl-2′-hydroxy-5,5′,6,6′-tetramethyl-1…
2017
The title compound, [Ti(C24H33O2)Cl3(C4H8O)], is a rare example of a trigonal–bipyramidal titanium coordination complex with three chloride and two oxygen donor ligands. The asymmetric unit contains two independent molecules having essentially the same conformation. The molecules feature the titanium(IV) metal cation complexed with three chloride ligands, a tetrahydrofuran molecule, and one oxygen atom from the resolved ligand precursor (R)-(+)-5,5′,6,6′-tetramethyl-3,3′-di-t-butyl-1,1′-biphenyl-2,2′-diol, where the remaining phenolic hydrogen atom engages in intermolecular O—H...Cl hydrogen bonding. In one molecule, the THF ligand is disordered over two orientations with refined site occup…
5-Acetyl-6-methyl-4-phenyl-1-(prop-2-ynyl)-3,4-dihydropyrimidin-2(1H)-one
2017
The 4-dihydropyrimidin-2(1H)-one moiety of the title molecule, C16H16N2O2, displays a half-chair conformation. The least-squares mean plane through this heterocycle is almost perpendicular to the aromatic ring [dihedral angle = 89.52 (8)°] and to the prop-2-ynyl chain [C—C—N—C torsion angle of −73.2 (2)°]. The mean plane through the acetyl group makes a dihedral angle of 30.93 (10)° with the mean plane of the heterocycle. There is an intramolecular C—H...O hydrogen bond forming anS(6) ring motif. In the crystal, molecules are linked by pairs of N—H...O hydrogen bonds forming inversion dimers.
A second solvatomorph of poly[[μ4-N,N′-(1,3,5-oxadiazinane-3,5-diyl)bis(carbamoylmethanoato)]nickel(II)dipotassium] : crystal structure, Hirshfeld su…
2021
The title compound, poly[triaquabis[μ4-N,N′-(1,3,5-oxadiazinane-3,5-diyl)bis(carbamoylmethanoato)]dinickel(II)tetrapotassium], [K4Ni2(C7H6N4O7)2(H2O)3] n , is a second solvatomorph of poly[(μ4-N,N′-(1,3,5-oxadiazinane-3,5-diyl)bis(carbamoylmethanoato)nickel(II)dipotassium] reported previously [Plutenko et al. (2021). Acta Cryst. E77, 298–304]. The asymmetric unit of the title compound includes two structurally independent complex anions [Ni(C7H6N4O7)]2−, which exhibit an L-shaped geometry and consist of two almost flat fragments perpendicular to one another: the 1,3,5-oxadiazinane fragment and the fragment including other atoms of the anion. The central Ni atom is in a square-planar N2O2 co…
Approximation of pore space with ellipsoids: a comparison of a geometrical method with a statistical one.
2018
International audience; We work with tomographic images of pore space in soil. The images have large dimensions and so in order to speed-up biological simulations (as drainage or diffusion process in soil), we want to describe the pore space with a number of geometrical primitives significantly smaller than the number of voxels in pore space. In this paper, we use the curve skeleton of a volume to segment it into some regions. We describe the method to compute the curve skeleton and to segment it with a simple segment approximation. We approximate each obtained region with an ellipsoid. The set of final ellipsoids represents the geometry of pore space and will be used in future simulations.…
Mechanical Detection of the De Haas–van Alphen Effect in Graphene
2022
Funding Information: We thank V. Falko, M. Kumar, and S. Paraoanu for useful discussions. This work was supported by the Academy of Finland projects 314448 (BOLOSE) and 336813 (CoE, Quantum Technology Finland) as well as by ERC (grant no. 670743). The research leading to these results has received funding from the European Unions Horizon 2020 Research and Innovation Programme, under Grant Agreement no 824109, and the experimental work benefited from the Aalto University OtaNano/LTL infrastructure. A.L. is grateful to Osk. Huttunen foundation for a scholarship. J.M. thanks the Väisälä Foundation of the Finnish Academy of Science and Letters for support. F.M. acknowledges financial support fr…
Geometry and quasisymmetric parametrization of Semmes spaces
2011
We consider decomposition spaces R 3 /G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R 3 /G constructed via modular embeddings of R 3 /G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R 3 /G×R m by R 3+m for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, on the defining sequences for R 3 /G. We give a necessary condition and a sufficient condition for the existence of such a parametrization. The necessary condition answers negatively a question of Heinone…
Environmental control on granular clinoforms of ancient carbonate shelves
2006
The purpose of this paper is to document the influence of depositional environments on shallow-water, low-relief clinoforms from the description of five ancient carbonate platforms: the Neoproterozoic (Namibia), Middle Jurassic (France), Lower Cretaceous (France), Upper Cretaceous (Oman) and Miocene (Turkey). These examples have been investigated on the basis of field observations. The clinoforms are described with reference to geometric and compositional attributes: declivity, shape, height, sedimentary structures, sediment fabric and components. The results show great variability in stratal geometry, declivity and facies distribution: (1) depositional profiles vary from exponential, to si…
Lipschitz Functions on Submanifolds of Heisenberg Groups
2022
Abstract We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on ${\mathbb {H}}$-rectifiable sets and a coarea formula on ${\mathbb {H}}$-rectifiable sets that completes the program started in [18].
Testing the Sobolev property with a single test plan
2020
We prove that in a vast class of metric measure spaces (namely, those whose associated Sobolev space is separable) the following property holds: a single test plan can be used to recover the minimal weak upper gradient of any Sobolev function. This means that, in order to identify which are the exceptional curves in the weak upper gradient inequality, it suffices to consider the negligible sets of a suitable Borel measure on curves, rather than the ones of the $p$-modulus. Moreover, on $\sf RCD$ spaces we can improve our result, showing that the test plan can be also chosen to be concentrated on an equi-Lipschitz family of curves.