Search results for "Geometry"
showing 10 items of 4487 documents
Fine tuning of the photophysical properties of cofacial diporphyrins via the use of different spacers
2002
The crystal and molecular structures of two unmetallated diporphyrin species using the biphenylene and dibenzofuran spacers, H4(DPB) and H4(DPO), respectively (DPB 4 − =1,8-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]biphenylene; DPO 4 − =4,6-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]dibenzofuran), are reported. These data are compared to their literature metallated analogs, stressing on the properties related to the flexibility of the ligands, ··· and M···M interactions. In addition, the lowest energy fluorescence properties of these non-phosphorescent diporphyrin compounds as well as three other related species, H4(DPA), H4(DPX), and H4(DPS) (DPA 4 − …
Thermodynamic and fluorescence emission studies on chemosensors containing anthracene fluorophores. Crystal structure of {[CuL1Cl]Cl}2·2H2O [L1 = N-(…
1999
The co-ordination capabilities toward hydrogen ions, Co2+, Ni2+, Cu2+, Zn2+ and Cd2+ of the novel receptor 2,6,9,13-tetraaza[14](9,10)anthracenophane (L) and of its open-chain counterpart N-(3-aminopropyl)-N′-3-(anthracen-9-ylmethyl)aminopropylethane-1,2-diamine (L1) is described. Stepwise protonation constants of the cyclic receptor (L) are lower than those of the open-chain receptor (L1) . Quenching effects of the fluorescence emission occur upon first and second deprotonation of L and upon second deprotonation of L1. Stability constants of the Co2+, Ni2+, Cu2+, Zn2+ and Cd2+ complexes follow the Irving–Williams trend and are intermediate between those of triethylenetetraamine with termin…
Statistical shape analysis of ascending thoracic aortic aneurysm: Correlation between shape and biomechanical descriptors
2020
An ascending thoracic aortic aneurysm (ATAA) is a heterogeneous disease showing different patterns of aortic dilatation and valve morphologies, each with distinct clinical course. This study aimed to explore the aortic morphology and the associations between shape and function in a population of ATAA, while further assessing novel risk models of aortic surgery not based on aortic size. Shape variability of n = 106 patients with ATAA and different valve morphologies (i.e., bicuspid versus tricuspid aortic valve) was estimated by statistical shape analysis (SSA) to compute a mean aortic shape and its deformation. Once the computational atlas was built, principal component analysis (PCA) allow…
Comparison and multiresolution analysis of irregular meshes with appearance attributes
2004
We present in this dissertation a method to compare and to analyse irregular meshes with appearance attributes. First, we propose a mesh comparison method using a new attribute deviation metric. Considered meshes contain geometric and appearance attributes (e.g. color, texture,temperature). The proposed deviation assessment allows the computation of local attribute differences between two meshes. We present an application of this method to mesh simplification algorithm quality assessment.Then we propose two multiresolution analysis schemes for irregular meshes with appearance attributes. First, a mesh is decomposed in a discret number of levels of detail. We introduce a surface geometry rel…
Wulff shape characterizations in overdetermined anisotropic elliptic problems
2017
We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.
Regular 1-harmonic flow
2017
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to Lipschitz initial data. We prove uniqueness and, in the case of a convex domain, local existence of solutions to the flow equations. If the target manifold has non-positive sectional curvature or in the case that the datum is small, solutions are shown to exist globally and to become constant in finite time. We also consider the case where the domain is a compact Riemannian manifold without boundary, solving the homotopy problem for 1-harmonic maps under some …
Best approximation and variational inequality problems involving a simulation function
2016
We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.
Mappings of finite distortion : size of the branch set
2018
Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.
Adaptive rational interpolation for point values
2019
Abstract G. Ramponi et al. introduced in Carrato et al. (1997,1998), Castagno and Ramponi (1996) and Ramponi (1995) a non linear rational interpolator of order two. In this paper we extend this result to get order four. We observe the Gibbs phenomenon that is obtained near discontinuities with its weights. With the weights we propose we obtain approximations of order four in smooth regions and three near discontinuities. We also introduce a rational nonlinear extrapolation which is also of order four in the smooth region of the given function. In the experiments we calculate numerically approximation orders for the different methods described in this paper and see that they coincide with th…
Numerical Study of Blow-Up Mechanisms for Davey-Stewartson II Systems
2018
We present a detailed numerical study of various blow-up issues in the context of the focusing Davey-Stewartson II equation. To this end we study Gaussian initial data and perturbations of the lump and the explicit blow-up solution due to Ozawa. Based on the numerical results it is conjectured that the blow-up in all cases is self similar, and that the time dependent scaling is as in the Ozawa solution and not as in the stable blow-up of standard $L^{2}$ critical nonlinear Schr\"odinger equations. The blow-up profile is given by a dynamically rescaled lump.