Search results for " Geometry"
showing 10 items of 2294 documents
On the Reception of Grassmann’s Work in Germany during the 1870’s
1996
It has often been remarked that Grassmann’s mathematics was not widely appreciated during his lifetime. Although awareness of the dimensions of his achievements began to spread in the early 1870’s, even in Germany relatively few mathematicians appear to have been well acquainted with either the original 1844 edition of Grassmann’s Ausdehnungslehre or the mathematically more accessible edition of 1862. The main reasons for this weak and rather delayed reception have been described often enough---Grassmann’s isolated working environment and his nearly impenetrable language---but there are a number of related aspects that still deserve closer consideration.1
Scenery Flow, Conical Densities, and Rectifiability
2015
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.
Complex tribomechanical characterization of ZnO nanowires: nanomanipulations supported by FEM simulations
2016
In the present work, we demonstrate a novel approach to nanotribological measurements based on the bending manipulation of hexagonal ZnO nanowires (NWs) in an adjustable half-suspended configuration inside a scanning electron microscope. A pick-and-place manipulation technique was used to control the length of the adhered part of each suspended NW. Static and kinetic friction were found by a 'self-sensing' approach based on the strain profile of the elastically bent NW during manipulation and its Young's modulus, which was separately measured in a three-point bending test with an atomic force microscope. The calculation of static friction from the most bent state was completely reconsidered…
The F-pure threshold of quasi-homogeneous polynomials
2018
Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .
Membrane distillation heat transfer enhancement by CFD analysis of internal module geometry
2011
Module geometry optimisation can be a crucial matter in all separation processes using selective or hydrophobic membranes, e.g. reverse osmosis (RO) and membrane distillation (MD). In fact the choice of suitable channel shape and size can dramatically affect the performance of the process. With reference to the membrane distillation process, temperature polarization phenomena and pres¬sure drops along the channels largely affect the process efficiency (i.e. the efficient use of temperature driving force for the passage of vapour through the membrane) as well as pressure distribution, module mechanical resistance and pumping costs. Several works have been presented so far in literature on th…
Carbon nanotube field-effect devices with asymmetric electrode configuration by contact geometry
2014
We have studied experimentally the conductive properties of single walled carbon nanotube (SWNT) based field-effect type devices, with different contact geometries at the connecting electrode. The device designs are asymmetric with one end of the SWNT having the metal electrode deposited on top and immersing it, while at the other end, the SWNT is on top of the electrode. The devices were made with either gold or palladium as electrode materials, of which the latter resulted in different behavior of the different contact types. This is argued to be caused by the existence of a thin insulating layer of surface adsorbents on the palladium, possibly Pd5O4, the effect of which is enhanced by th…
[Cu(P^P)(N^N)][PF6] compounds with bis(phosphane) and 6-alkoxy, 6-alkylthio, 6-phenyloxy and 6-phenylthio-substituted 2,2'-bipyridine ligands for lig…
2018
We report a series of [Cu(P^P)(N^N)][PF6] complexes with P^P = bis(2-(diphenylphosphino)phenyl)ether (POP) or 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene (xantphos) and N^N = 6-methoxy-2,2′-bipyridine (MeObpy), 6-ethoxy-2,2′-bipyridine (EtObpy), 6-phenyloxy-2,2′-bipyridine (PhObpy), 6-methylthio-2,2′-bipyridine (MeSbpy), 6-ethylthio-2,2′-bipyridine (EtSbpy) and 6-phenylthio-2,2′-bipyridine (PhSbpy). The single crystal structures of all twelve compounds have been determined and confirm chelating modes for each N^N and P^P ligand, and a distorted tetrahedral geometry for copper(I). For the xantphos-containing complexes, the asymmetrical bpy ligand is arranged with the 6-substituent lying …
Complexes of titanium and zirconium containing a tridentate linked amido–cyclopentadienyl ligand with a soft donor group: synthesis, structure, and e…
1999
Abstract Group 4 metal complexes M(η5:η1-C5R4SiMe2NCH2CH2SMe)Cl2 (R=H, M=Ti; R=Me, M=Ti, Zr) containing the thioether-functionalized linked amido–cyclopentadienyl ligand were synthesized and characterized by 1H- and 13C-NMR spectroscopy, mass spectrometry, and elemental analysis. The crystal structures of the complexes Ti(η5:η1-C5H4SiMe2NCH2CH2SMe)Cl2 and Zr(η5:η1:η1-C5Me4SiMe2NCH2CH2SMe)Cl2 were determined by single-crystal X-ray diffraction studies. The titanium complex is a conventional three-legged piano-stool molecule without an intramolecular interaction between the sulfur donor group and the titanium center, whereas the zirconium complex adopts a trigonal bipyramidal structure, with …
Zirconium and hafnium complexes of the thio(bisphenolato) ligand: synthesis, structural characterization and testing as 1-hexenepolymerizationcatalys…
2009
Thio(bisphenolato) complexes of the type [M2(mu-tbop-kappa3O,S,O)2Cl4] [M = Zr 1, Hf 2 and tbop = 2,2-thiobis{4-(1,1,3,3-tetramethyl-butyl)phenolate}] were prepared by HCl elimination from tbopH2 and MCl4. Substitution of the chlorides in 1 and 2 by 2,6-diisopropylphenolato groups (dipp) generates new compounds [M2(mu-tbop-kappa3O,S,O)2(dipp)4] (M = Zr 3, Hf 4). The structures of 1-4 were confirmed by NMR spectroscopy; complexes 3 and 4 were further investigated by X-ray crystallography. These studies showed 1-4 to be dimers either in the solid state or in solution and to have metal centers adopting distorted octahedral geometry. However treatment of MCl4 with [Al2(mu-OEt)2(tbop-kappa3O,S,O…
Extending CSG with projections: Towards formally certified geometric modeling
2015
We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…