Search results for " Geometry."
showing 10 items of 2189 documents
R Code for Hausdorff and Simplex Dispersion Orderings in the 2D Case
2010
This paper proposes a software implementation using R of the Hausdorff and simplex dispersion orderings. A copy can be downloaded from http://www.uv.es/~ayala/software/fun-disp.R . The paper provides some examples using the functions exactHausdorff for the Hausdorff dispersion ordering and the function simplex for the simplex dispersion orderings. Some auxiliary functions are commented too.
Convexly generic curves in R 3
1988
We study curves immersed in R 3, with special interest in the description of their convex hull frontier structure from a global viewpoint. Genericity conditions are set for these curves by looking at the singularities of height functions on them. We define panel structures for convexly generic curves and work out numerical relations involving the number of tritangent support planes. As a consequence, a generic version of the 4-vertex theorem for convex curves in R 3 is obtained.
Shape-Based Features for Cat Ganglion Retinal Cells Classification
2002
This article presents a quantitative and objective approach to cat ganglion cell characterization and classification. The combination of several biologically relevant features such as diameter, eccentricity, fractal dimension, influence histogram, influence area, convex hull area, and convex hull diameter are derived from geometrical transforms and then processed by three different clustering methods (Ward’s hierarchical scheme, K-means and genetic algorithm), whose results are then combined by a voting strategy. These experiments indicate the superiority of some features and also suggest some possible biological implications.
Macrocycle-Based Spin-Crossover Materials
2009
International audience; New iron(II) complexes of formula [Fe(L1)](BF(4))(2) (1) and [Fe(L2)](BF(4))(2) x H(2)O (2) (L1 = 1,7-bis(2'-pyridylmethyl)-1,4,7,10-tetraazacyclododecane; L2 = 1,8-bis(2'-pyridylmethyl)-1,4,8,11-tetraazacyclotetradecane) have been synthesized and characterized by infrared spectroscopy, variable-temperature single-crystal X-ray diffraction, and variable-temperature magnetic susceptibility measurements. The crystal structure determinations of 1 and 2 reveal in both cases discrete iron(II) monomeric structures in which the two functionalized tetraazamacrocycles (L1 and L2) act as hexadentate ligands; the iron(II) ions are coordinated with six nitrogen atoms: four from …
Versatility and dynamics of the copper(I) coordination sphere in sterically hindering tris(pyrazolyl)methane-incorporating macrobicycles
2009
Two arene-capped macrobicycles (1 and 2) incorporating the tris(pyrazolyl)methane (Tpm) chelate have been prepared from a benzylthiol-functionalized Tpm precursor (3). Reaction of either macrobicycle with Cu(CH3CN)4+ leads to tetrahedral or trigonal-planar, fluxional complexes incorporating the Cu(CH3CN)+ subunit ([Cu(1)(CH3CN)]+ and [Cu(2)(CH3CN)]+). The acetonitrile ancillary ligand does not fit inside the macrobicycle cavity and can be removed by heating under vacuum, which produces the [Cu(1)]+ and [Cu(2)]+ species probably involving intramolecular thioether coordination. The [Cu(1)(CH3CN)]+ complex was shown to convert slowly in wet acetone into a helical coordination polymer, which is…
Copper(II) complexes of 1,4,5,8,9,12-hexaazatriphenylene with oxalate, squarate, perchlorate as auxiliary ligands or counter ion
2002
Abstract The crystal structures of [Cu(hat)(H2O)(ox)]·H2O (I), [Cu(hat)(H2O)3(sq)]·3H2O (II) and [Cu(hat)(H2O)2](ClO4)2·4H2O (III) have been determined from X-ray single crystal diffraction data (hat=1,4,5,8,9,12-hexaazatriphenylene, ox=oxalate, sq=squarate=dianion of 3,4-dihydroxy-cyclobut-3-ene-1,2-dione). Compound I crystallises in the triclinic system, space group P 1 with a=6.6626(10), b=9.2001(14), c=12.9954(19) A , α=103.301(15), β=91.414(21), γ=105.523(13)°, Z=2; compound II in the orthorhombic system, space group P212121 with a=6.9274(2), b=8.4327(3), c=34.0577(14) A , Z=4; and compound III in the monoclinic system, space group C2/c with a=22.6652(10), b=9.2220(10), c=16.1400(10) A…
Oxidovanadium(V) Complexes with Aminoethanol Bis(phenolate) [O,N,O,O] Ligands: Preparations, Structures, N-Dealkylation and Condensation Reactions
2011
The reactions between [VO(acac)2] (acac– = acetylacetonate ion) or [VO(OPr)3] and trianionic tetradentate N,N-bis(2-methylene-4,6-alkylphenolate)aminoethanolate ligands, [L13– (4,6-dimethyl), L23– (4-methyl, 6-tert-butyl), L33– (4-tert-butyl, 6-methyl), L43– (4,6-di-tert-butyl)], afford mononuclear complexes [VO(L1)] (1) and [VO(L2)] (2) with a trigonal bipyramidal coordination sphere around the VV ion, or dinuclear octahedral complexes [V2O2(L3)2] (3) and [V2O2(L4)2] (4). In methanol an adduct with the formula [VO(L1)(MeOH)]·1/2MeOH (5) is obtained. According to multinuclear NMR spectroscopy all those complexes have a mononuclear structure in CDCl3 solutions. In wet polar solvents complex …
Elementary Integration of Superelliptic Integrals
2021
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.
Granulometric moments and corneal endothelium status
2001
Abstract Specular microscopy is a common practice in Ophthalmology. The corneal endothelium status is usually evaluated by means of the density, the hexagonality, the mean, the standard deviation and the coefficient of variation of cell areas. We propose to replace the cell area moments by the corresponding moments of a different probability distribution, the granulometric size distribution associated to a disc. All cells touching the frame are ignored by the area moments but used by the granulometric moments. Twenty images have been analyzed. When the size of the focused region is reduced, the area moments show a greater variation than the corresponding granulometric moments.
Granulometric analysis of corneal endothelium specular images by using a germ–grain model
2007
Specular microscopy is widely used to study the human corneal endothelium status in vivo. In this paper, the corneal endothelium is represented as a binary image composed of the cell inscribed circles. The granulometric distribution function of the complement of this image is used as a functional descriptor, which provides information about the shape, size and spatial arrangement of cells. Experimental evaluation using bootstrap techniques shows its ability to discriminate between controls and pathological cases. It represents a reliable and graphical alternative to the classical indices (cell density, hexagonality and coefficient of variation of cell areas), which behave poorly when detect…