Search results for "Geometry"
showing 10 items of 4487 documents
[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 …
Bounds to internal forces for elastic-plastic solids subjected to variable loads
1979
Considering an elastic-plastic workhardening solid with piecewise linear yield surfaces and a piecewise linear workhardening law, we give a method for constructing bounds to the internal forces and to the (hardened) yield stresses produced by the action of variable loads at any point of the body and at any time. The loading history is supposed to be unknown, but the loads range within a given domain.
Shakedown theorems for elastic–plastic solids in the framework of gradient plasticity
2008
Abstract Static and kinematic shakedown theorems are given for a class of generalized standard materials endowed with a hardening saturation surface in the framework of strain gradient plasticity. The so-called residual-based gradient plasticity theory is employed. The hardening law admits a hardening potential, which is a C 1 -continuous function of a set of kinematic internal variables and of their spatial gradients, and is required to satisfy a global sign restriction (but not to be necessarily convex). The totally produced, the accumulated and the freely moving dislocations per unit volume, distinguished as statistically stored and geometrically necessary ones, are in this way accounted…
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,…
Toward Approximate GML Retrieval Based on Structural and Semantic Characteristics
2010
International audience; GML is emerging as the new standard for representing geographic information in GISs on the Web, allowing the encoding of structurally and semantically rich geographic data in self describing XML-based geographic entities. In this study, we address the problem of approximate querying and ranked results for GML data and provide a method for GML query evaluation. Our method consists of two main contributions. First, we propose a tree model for representing GML queries and data collections. Then, we introduce a GML retrieval method based on the concept of tree edit distance as an efficient means for comparing semi-structured data. Our approach allows the evaluation of bo…
Bords d'une surface médiane : Identifications et applications
2014
National audience; Un squelette d'une forme fermée est une structure mince, centrée dans cette forme, décrivant sa topologie et sa géométrie. Les squelettes permettent de développer des applications interactives en synthèse d'images~: l'utilisateur peut manipuler intuitivement des formes en modifiant leurs squelettes. Parmi toutes les formulations de squelettes, nous nous intéressons en particulier à la surface médiane. Ses éléments, nommés atomes, sont les sphères maximales intérieures à la forme décrite. Les positions des atomes sont organisées en courbes et surfaces, qui composent la structure squelettale. Cette structure peut être d'une grande aide pour manipuler une forme. Cependant, e…
Fractional half-tangent of a curve described by Iterated Function Systems.
2009
International audience; The deterministic fractal curves and surfaces find many applications in modeling of rough objects. However, these curves and surfaces are nowhere differentiable. Without notion of tangent, we can not determine the relative orientation of two fractal shapes, to join them with a "natural" aspect. Various works proposed a generalization of the concept of derivative by introducing the fractional derivative. In this paper we apply this concept of fractional derivative to the curves described by Iterated Function Systems. We show that if the fractional derivative exists at boundary points of the curve, the direction of the fractional half-tangent is necessarily the eigenve…
Tangentes à une courbe fractale
2007
http://www.irit.fr/REFIG/index.php/refig/article/view/10; National audience; Nous nous intéressons au calcul des tangentes à une courbe fractale définie à l'aide d'un IFS. Généralement, les courbes fractales sont nulle part dérivables, mais sous certaines conditions on peut montrer qu'elles admettent, en un ensemble de points, des demi-tangentes à droite et à gauche. Nous proposons une méthode permettant de déterminer ces demi-tangentes.