Search results for " geometry"

Bézier surfaces of minimal area: The Dirichlet approach

2004

The Plateau-Bezier problem consists in finding the Bezier surface with minimal area from among all Bezier surfaces with prescribed border. An approximation to the solution of the Plateau-Bezier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bezier surfaces obtained by the use of masks related with minimal surfaces are studied.

Index-based triangulation method for efficient generation of large three-dimensional ultrasonic C-scans

2018

The demand for high-speed ultrasonic scanning of large and complex components is driven by a desire to reduce production bottlenecks during the non-destructive evaluation (NDE) of critical parts. Emerging systems (including robotic inspection) allow for the collection of large volumes of data in short time spans, compared to existing inspection systems. To maximise throughput, it is crucial that the reconstructed inspection datasets are generated and evaluated rapidly without loss of detail. This requires new data visualisation and analysis tools capable of mapping complex geometries while guaranteeing full coverage. This paper presents an entirely new approach for the visualisation of thre…

Infinitesimal Hilbertianity of Locally CAT(κ)-Spaces

2021

We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space (Y,d,μ)(Y,d,μ) is infinitesimally Hilbertian, i.e. the Sobolev space W1,2(Y,d,μ)W1,2(Y,d,μ) is a Hilbert space. The result is obtained by constructing an isometric embedding of the ‘abstract and analytical’ space of derivations into the ‘concrete and geometrical’ bundle whose fibre at x∈Yx∈Y is the tangent cone at x of YY. The conclusion then follows from the fact that for every x∈Yx∈Y such a cone is a CAT(0)CAT(0) space and, as such, has a Hilbert-like structure. peerReviewed

Spectroscopic, crystal structural, theoretical and biological studies of phenylacetohydrazide Schiff base derivatives and their copper complexes

2020

Two phenylacetohydrazide Schiff base derivatives: N’-(1-(2-hydroxyphenyl)ethylidene)-2-phenylacetohydrazide, HL1, and N’-((1-hydroxynaphthalen-2-yl)methylene)-2-phenylacetohydrazide, HL2, were synthesized. HL1 dimerizes in presence of HCl, probably via radical mechanism to give (2,2’-((1E)-hydrazine-1,2-diylidenebis(ethan-1-yl-1-ylidene))diphenol (DIM). Thermal reactions of Cu(II) ions with the two Schiff base ligands resulted in formation of the binuclear complexes [(CuL1)2] and [(CuL2)2]. The stoichiometry and structures of the reported compounds were investigated by several spectroscopic and analytical techniques. The structure of the HL1 ligand and its complex [(CuL1)2] as well as the D…

Quantum interference and the time-dependent radiation of nanojunctions

2021

Using the recently developed time-dependent Landauer-B\"uttiker formalism and Jefimenko's retarded solutions to the Maxwell equations, we show how to compute the time-dependent electromagnetic field produced by the charge and current densities in nanojunctions out of equilibrium. We then apply this formalism to a benzene ring junction, and show that geometry-dependent quantum interference effects can be used to control the magnetic field in the vicinity of the molecule. Then, treating the molecular junction as a quantum emitter, we demonstrate clear signatures of the local molecular geometry in the non-local radiated power.

Il fondo Maria Del Re e l’insegnamento della Geometria nell’Universita’ di Napoli negli anni Venti e Trenta del Novecento

2014

Phase diagram of polymer blends in confined geometry

2001

Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding smei-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surfaces fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exh…

Substituent effect of nitro group on aromaticity of carbazole rings

2014

The molecular geometries of carbazole and its 17 nitro derivatives were optimized at the B3LYP/6-311++G(2d,2p) level of theory. The harmonic oscillator model of aromaticity and nucleus-independent chemical shift descriptors of π-electron delocalization were calculated to estimate the aromaticity of the carbazole five- and six-membered rings. The biggest changes in the value of both descriptors were observed for the pyrrole ring. The nitro group attached to 3 and/or 6 positions of the carbazole ring system exerts only a slight influence on the benzene ring aromaticity.

Association of Arsenic Exposure With Cardiac Geometry and Left Ventricular Function in Young Adults

2019

Background: Arsenic exposure has been related to numerous adverse cardiovascular outcomes. The aim of this study was to investigate the cross-sectional and prospective association between arsenic exposure with echocardiographic measures of left ventricular (LV) geometry and functioning. Methods: A total of 1337 young adult participants free of diabetes mellitus and cardiovascular disease were recruited from the SHFS (Strong Heart Family Study). The sum of inorganic and methylated arsenic concentrations in urine (ΣAs) at baseline was used as a biomarker of arsenic exposure. LV geometry and functioning were assessed using transthoracic echocardiography at baseline and follow-up. Results: Mea…

Space of signatures as inverse limits of Carnot groups

2021

We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.…