Search results for " Geometry."

Experimental and theoretical studies of the molecular and crystal structures of trialkoxy- and chlorodialkoxy-stibanes

2001

The molecular structures of triisopropoxystibane, Sb((OPr)-Pr-i)(3), and chlorodiisopropoxystibane, SbCl((OPr)-Pr-i)(2), were determined in the solid state by single crystal X-ray diffraction. Sb((OPr)-Pr-i)(3) forms discrete centrosymmetric dimers in the solid state via Sb . . .O-Sb interactions, leading to pseudo trigonal bipyramidal configurations of the four co-ordinate Sb atoms, while SbCl((OPr)-Pr-i)(2) forms chains via Sb . . .O-Sb and Sb . . . Cl-Sb bridges, resulting in five-co-ordinate Sb atoms with pseudo octahedral configurations. Comparison of the solid state structures and the density functional optimized molecular structures of Sb(OMe)(3), SbCl(OMe)(2) and their dimers reveal…

Influence of Structural Isomerism on the Electronic Properties of Extended Phthalocyanines

1993

Abstract The electronic structure of isomeric naphthalocyanines (H2Nc) is investigated using the nonempirical valence effective Hamiltonian (VEH) technique. The way the outer benzene rings are annelated (linearly as in 2,3-H2Nc or angularly as in 1,2-H2Nc) is shown to determine very important changes in the electronic properties. While similar properties to those of phthalocyanine are calculated for 1,2-H2Nc, lower oxidation potentials and red-shifted optical absorptions are predicted for 2,3-H2Nc in agreement with experimental data. The isomerism resulting from the different relative positions of the angularly annelated benzene rings in 1,2-H2Nc is shown to have almost no effect on the ele…

Bounded Geometry, Growth and Topology

2011

A method to reduce the FP/imm number through CC and MLO views comparison in mammographic images

2008

In this paper we propose a method to reduce the FP/imm number through CC and MLO mammographic views comparison of the same patient. The proposed solution uses the symmetry properties of the breast to compute a geometric transformation that permits to represent the two images in comparable coordinates systems. Through this method, potential pathological ROIs of one of the projections are correlated with the ROIs in the second view. To show the effectiveness of the result we apply the method on a dataset composed of 112 couples of pathological images. Experiments shows that method enables a reduction by up to 700/0 of the FP/imm number detected after the classification step

Über zinn-haltige heterocyclen

1981

Abstract A complete series of diphenyl and mixed methyl/chlorine/bromine/iodinephenyl substituted oxadithia- and trithiastannocanes has been prepared by reactions between the respective disodium dithiolates and tin dihalides. The 13C NMR chemical shifts of these compounds and the coupling constants J(119Sn13C) are dependent upon the magnetic anisotropy of the substituents and the bond angles at the tin atom. The crystal structure of 2,2-diphenyl-1,3,6-trithia-2-stannocane has been determined and refined to R = 0.039. The environment of Sn is a monocapped tetrahedron (transannular distance Sn⋯S 324.6(1) pm). This type of coordination, intermediate between a tetrahedron and a trigonal bipyra…

Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique

2006

Dupin cyclides were introduced in 1822 by the French mathematician C-P. Dupin. They are algebraic surfaces of degree 3 or 4. The set of geometric properties of these surfaces has encouraged an increasing interest in using them for geometric modeling. A couple of algorithmes is already developed to convert a Dupin cyclide patch into a rational biquadratic Bezier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bezier patch into a Dupin cyclide one, and we present a conversion algorithm to compute the parameters of a Dupin cyclide with the boundary of the patch that corresponds to the given Bezier patch.

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…