Search results for " geometry"
showing 10 items of 2294 documents
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…
Real Algebraic Geometry
2011
144 Pages; Cet ouvrage constitue les actes de la conférence de Géométrie Algébrique Réelle qui a eu lieu à Rennes du 20 au 24 Juin 2011
A rigidity theorem for the pair ${\cal q}{\Bbb C} P^n$ (complex hyperquadric, complex projective space)
1999
Given a compact Kahler manifold M of real dimension 2n, let P be either a compact complex hypersurface of M or a compact totally real submanifold of dimension n. Let \(\cal q\) (resp. \({\Bbb R} P^n\)) be the complex hyperquadric (resp. the totally geodesic real projective space) in the complex projective space \({\Bbb C} P^n\) of constant holomorphic sectional curvature 4\( \lambda \). We prove that if the Ricci and some (n-1)-Ricci curvatures of M (and, when P is complex, the mean absolute curvature of P) are bounded from below by some special constants and volume (P) / volume (M) \(\leq \) volume (\(\cal q\))/ volume \(({\Bbb C} P^n)\) (resp. \(\leq \) volume \(({\Bbb R} P^n)\) / volume …
Analysis of static friction and elastic forces in a nanowire bent on a flat surface: A comparative study
2014
ZnO nanowires bent to a complex shape and held in place by static friction force from supporting flat surface are investigated experimentally and theoretically. The complex shapes are obtained by bending the nanowires inside a scanning electron microscope with a sharp tip attached to a nanopositioner. Several methods previously described in the literature are applied along with author's original method to calculate the distributed friction force and stored elastic energy in the nanowires from the bending profile. This comparative study evidences the importance of the usage of appropriate models for accurate analysis of the nanowires profile. It is demonstrated that incomplete models can lea…
Magnetic coupling and spin topology in linear oxalato-bridged tetranuclear chromium(III)–copper(II) complexes with aromatic diimine ligands
2013
Abstract A novel heterotetranuclear chromium(III)–copper(II) complex of formula {[CrIII(bpy)(ox)2]2CuII2(bpy)2(ox)}·6H2O (1) has been synthesized by the ligand exchange reaction between Ph4P[CrIII(bpy)(ox)2]·H2O and [CuII(bpy)2(NO3)]NO3·MeOH in methanol (bpy = 2,2′-bipyridine; ox2− = oxalate dianion). The X-ray crystal structure of 1 consists of neutral oxalato-bridged CrIII2Cu2II zigzag entities which are formed by the monodentate coordination of two [CrIII(bpy)(ox)2]− mononuclear anionic units through one of its two oxalato groups toward a [CuII2(bpy)2(ox)]2+ dinuclear cationic moiety featuring relatively long axial bonds at the square pyramidal CuII ions. Variable temperature (2.0–300 K)…
The geometry of corank 1 surfaces in ℝ4
2018
Abstract We study the geometry of surfaces in ℝ4 with corank 1 singularities. For such surfaces, the singularities are isolated and, at each point, we define the curvature parabola in the normal space. This curve codifies all the second-order information of the surface. Also, using this curve, we define asymptotic and binormal directions, the umbilic curvature and study the flat geometry of the surface. It is shown that we can associate to this singular surface a regular one in ℝ4 and relate their geometry.
Theoretical study of the molecular structure and the stability of neutral and reduced tetracyanoethylene
2003
Abstract The molecular structure and the stability of neutral, anionic, and dianionic tetracyanoethylene (TCNE) have been studied with MP2, coupled-cluster (CC), and density functional theory (DFT) procedures. The optimized geometries are in agreement with the available experimental data, although significant deviations for the CN bond distance have been obtained at the MP2 level. The adiabatic electron affinity of TCNE calculated with the B3LYP method is overestimated by 0.32 eV. In the light of the CC results, the source of such an overestimation is suggested to lie on the theoretical approach, rather than on a too low experimental value.
Muon physics — Survey
1992
The empirical basis of the minimal standard model has been consolidated in an impressive way, over the last seventeen years, by precision experiments at the meson factories. I illustrate this by means of selected examples of muonic weak interaction processes. I then describe an extension of Yang-Mills theory, inspired by noncommutative geometry, that yields precisely the standard model but fixes and explains some of its empirical input. In particular, this new approach yields a simple geometrical interpretation of spontaneous symmetry breaking. The algebraic framework of this approach offers a natural place for the lepton and quark matter fields and for inter-family mixing.
Continuum Monte Carlo simulation of phase transitions in rod-like molecules at surfaces
1994
Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of th…
Crystal structure of bis(cyclohexylammonium) diphenyldioxalatostannate(IV)
2015
In the title salt, (CyNH3)2[Sn(Ph2)(C2O4)2] (Cy is cyclohexyl and Ph is phenyl), the SnPh2 moiety is chelated by two oxalate anions, leading to a cis arrangement within the distorted octahedral coordination sphere of the SnIV atom.