Search results for " Geometry"
showing 10 items of 2294 documents
Magneto-structural correlations in asymmetric oxalato-bridged dicopper(II) complexes with polymethyl-substituted pyrazole ligands
2018
Two oxalato-bridged dinuclear copper(II) complexes, [{Cu(Hdmpz)3}2(μ-ox)](ClO4)2·2H2O (1) and [{Cu(Htmpz)3}2(μ-ox)](ClO4)2·2H2O (2) (Hdmpz = 3,5-dimethyl-1H-pyrazole and Htmpz = 3,4,5-trimethyl-1H-pyrazole), have been synthesized and structurally and magnetically characterized. The crystal structures of 1 and 2 consist of asymmetric bis-bidentate μ-oxalatodicopper(II) complex cations with two short [Cu–O = 1.976(2) (1) and 1.973(2) Å (2)] and two long copper–oxygen bonds [Cu–O = 2.122(2) (1) and 2.110(2) Å (2)]. The environment at each CuII ion in 1 and 2 is closer to the trigonal bipyramidal geometry than to the square pyramidal [τ = 0.633 (1) and 0.711 (2)]. The magnetic properties of 1 a…
Synthesis, crystal structure and magnetic properties of the cyclic tetranuclear compound [Cu4(pz)4(hppa)2(H2O)4] [pz = pyrazolate; hppa = R,S-2-hydro…
2019
Abstract The synthesis, X-ray structure and magnetic properties of the neutral tetranuclear copper(II) complex of formula [Cu4(pz)4(hppa)2(H2O)4] (1) [Hpz = pyrazole and hppa = R,S-2-hydroxo-2-phenyl-2-(1-pyrazolyl)acetate] are reported. Remarkably, the structure of 1 reveals the presence of the S- and R-forms of the new hppa ligand which is formed in situ in the complex reaction between copper(II), pyrazole and phenylmalonate in water:methanol solvent mixture under ambient conditions. The two crystallographically independent copper(II) ions [Cu(1)/Cu(2)] are five-coordinate in square pyramidal surroundings. Three nitrogen atoms, from two pz groups and one hppa ligand and one oxygen atom of…
Complex geometry and kinematics of subsidiary faults within a carbonate-hosted relay ramp
2019
Abstract Minor fault geometry and kinematics within relay ramps is strongly related to the stress field perturbations that can be produced when two major fault segments overlap and interact. Here we integrate classical fieldwork and interpretation of a virtual outcrop to investigate the geometry and kinematics of subsidiary faults within a relay ramp along the Tre Monti normal fault in the Central Apennines. Although the Tre Monti fault strikes parallel to the regional extension (NE-SW) it shows predominant dip-slip kinematics, suggesting a NW-SE oriented extension acting at sub-regional scale (1–10 km). Conversely, the slickenlines collected on the front segment of the relay ramp highlight…
Modelling Complex Volume Shape Using Ellipsoid: Application to Pore Space Representation
2017
Natural shapes have complex volume forms that are usually difficult to model using simple analytical equations. The complexity of the representation is due to the heterogeneity of the physical environment and the variety of phenomena involved. In this study we consider the representation of the porous media. Thanks to the technological advances in Computed Topography scanners, the acquisition of images of complex shapes becomes possible. However, and unfortunately, the image data is not directly usable for simulation purposes. In this paper, we investigate the modeling of such shapes using a piece wise approximation of image data by ellipsoids. We propose to use a split-merge strategy and a…
Metric Rectifiability of ℍ-regular Surfaces with Hölder Continuous Horizontal Normal
2021
Abstract Two definitions for the rectifiability of hypersurfaces in Heisenberg groups $\mathbb{H}^n$ have been proposed: one based on ${\mathbb{H}}$-regular surfaces and the other on Lipschitz images of subsets of codimension-$1$ vertical subgroups. The equivalence between these notions remains an open problem. Recent partial results are due to Cole–Pauls, Bigolin–Vittone, and Antonelli–Le Donne. This paper makes progress in one direction: the metric Lipschitz rectifiability of ${\mathbb{H}}$-regular surfaces. We prove that ${\mathbb{H}}$-regular surfaces in $\mathbb{H}^{n}$ with $\alpha $-Hölder continuous horizontal normal, $\alpha> 0$, are metric bilipschitz rectifiable. This impr…
LMI-based 2D-3D Registration: from Uncalibrated Images to Euclidean Scene
2015
International audience; This paper investigates the problem of registering a scanned scene, represented by 3D Euclidean point coordinates , and two or more uncalibrated cameras. An unknown subset of the scanned points have their image projections detected and matched across images. The proposed approach assumes the cameras only known in some arbitrary projective frame and no calibration or autocalibration is required. The devised solution is based on a Linear Matrix Inequality (LMI) framework that allows simultaneously estimating the projective transformation relating the cameras to the scene and establishing 2D-3D correspondences without triangulating image points. The proposed LMI framewo…
A laplace type problem for three lattices with non-convex cell
2016
In this paper we consider three lattices with cells represented in Fig. 1, 3 and 5 and we determine the probability that a random segment of constant length intersects a side of lattice. c ⃝2016 All rights reserved.
Real-time biomechanical modeling of the liver using Machine Learning models trained on Finite Element Method simulations
2020
[EN] The development of accurate real-time models of the biomechanical behavior of different organs and tissues still poses a challenge in the field of biomechanical engineering. In the case of the liver, specifically, such a model would constitute a great leap forward in the implementation of complex applications such as surgical simulators, computed-assisted surgery or guided tumor irradiation. In this work, a relatively novel approach for developing such a model is presented. It consists in the use of a machine learning algorithm, which provides real-time inference, trained on tens of thousands of simulations of the biomechanical behavior of the liver carried out by the finite element me…
Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
2020
We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with a strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all Casimirs linear in momenta on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented. peerReviewed
On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1
2016
Abstract Let f : X → P 1 be a non-isotrivial family of semi-stable curves of genus g ≥ 1 defined over an algebraically closed field k. Denote by s nc the number of the singular fibers whose Jacobians are non-compact. We prove that s nc ≥ 5 if k = C and g ≥ 5 ; we also prove that s nc ≥ 4 if char ( k ) > 0 and the relative Jacobian of f is non-smooth.