Search results for " geometry"
showing 10 items of 2294 documents
Quasisymmetric spheres over Jordan domains
2015
Let $\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\Sigma$ defined by graphs of functions of $dist( \cdot ,\partial \Omega)$ over $\Omega$. The goal is to find the right conditions on the geometry of the base $\Omega$ and the growth of the height so that $\Sigma$ is a quasisphere, or quasisymmetric to $\mathbb{S}^2$. An internal uniform chord-arc condition on the constant distance sets to $\partial \Omega$, coupled with a mild growth condition on the height, gives a close-to-sharp answer. Our method also produces new examples of quasispheres in $\mathbb{R}^n$, for any $n\ge 3$.
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
Our Friend and Mathematician Karl Strambach
2020
This paper is dedicated to Karl Strambach on the occasion of his 80th birthday. Here we want to describe our work with Prof. Karl Strambach.
A study of dimethyltin(IV)-L-cysteinate in aqueous solution
1988
The in vivo activity of some R2Sn-L-cysteinate complexes (R = Me, Et, n-Bu) against murine P-388 leukaemia has been tested. Only the Et2Sn(IV) complex showed a marginal positive effect. Trigonal bipyramidal tin environments with two carbon (R) atoms and the sulfur atom in the equatorial plane and oxygen (carboxylate) and nitrogen (NH2) in apical positions have been proposed for the solid compexes (R = Me, Et, n-Bu, Ph) on the basis of experimental Mossbauer parameters and infrared (IR) data. Aqueous solutions of the Me2SnL-cysteinate have been studied by IR, 1H NMR and 119Sn Mossbauer spectroscopy (in frozen solution) at different pH values to identify the Me2Sn(IV) species present. At pH >…
Stabilities and coordination modes of histidine in copper(II) mixed-ligand complexes with ethylenediamine, diethylenetriamine or N,N,N′,N″,N″-pentame…
2008
Abstract Solution equilibrium studies on the Cu(II)–polyamine–methionine ternary systems (polyamine: ethylenediamine (en), diethylenetriamine (dien), N,N,N′,N′′,N′′-pentamethyldiethylenetriamine (Me5dien)) have been performed by pH-potentiometry, UV–Vis spectrophotometry and EPR methods. The obtained results suggest the formation of the mixed-ligand complexes with [Cu(A)(Met)]+ stoichiometry in all studied systems. Our spectroscopic results indicate the tetragonal geometry for [Cu(en)(Met)]+, the geometry slightly deviated from square pyramidal for [Cu(dien)(Met)]+ and strongly deviated from square pyramidal towards trigonal bipyramidal for the [Cu(Me5dien)(Met)]+ species. The coordination …
INTERACTIONS OF ORGANOTIN(IV) HALIDES WITH REDUCED GLUTATHIONE IN AQUEOUS-SOLUTION
1993
Abstract Glutathione (GSH) is a compound extremely common among many living organisms in which it plays a fundamental role in the processes of detoxification. Also, organotin(IV) derivatives are more and more commonly used in technological processes or as antitumor drugs. So it seemed interesting to investigate the possible interactions between GSH and organotin compounds in water. Particularly, it has been studied because of its role in the organic radicals linked to the tin center on the stoichiometry and the structure of the adducts. Information was obtained following the reaction between Me n SnCl 4-n (n = 1 to 3) and GSH by Mossbauer and NMR spectroscopies on the assumption that change…
New cyclic tetranuclear copper(II) complexes containing quadrilateral cores: Synthesis, structure, spectroscopy and their interactions with DNA in aq…
2017
Abstract Three new cyclic tetranuclear copper(II) complexes, Tetrakis{3-[(2-pyridylmethyl)-amino]-propionato}(tetrachloro)tetracopper(II)methanolhydrate (1·CH3OH·H2O), Tetrakis{3-[(2-pyridylmethyl)-amino]-propionato}(tetrathiocyanato)tetracopper(II) (2) and Tetrakis{3-[(2-pyridylmethyl)-amino]-propionato}(tetraazido)tetracopper(II) (3) have been synthesized by exploiting the chelating ability and bridging potential of a carboxyamine functionalized tridentate ligand, HL (HL = 3-[(2-Pyridylmethyl)-amino]-propionic acid). Complexes 1, 2 and 3 have been synthesized by carrying out reaction of the ligand HL with stoichiometric amounts of CuCl2·2H2O, CuCl2·2H2O/NH4SCN, and CuCl2·2H2O/NaN3, respec…
Copper(II)-assisted hydrolysis of 2,4,6-tris(2-pyrimidyl)-1,3,5-triazine (tpymt): syntheses, crystal structures and magnetic properties of [Cu(bpcam)…
2005
Abstract The reaction of the 2,4,6-tris(2-pyrimidyl)-1,3,5-triazine (tpymt) ligand with copper(II) perchlorate or sulfate in aqueous solution affords complexes [Cu(bpcam)(H2O)2]ClO4 · 3H2O (1), [Cu(bpcam)(H2O)2][Cu(bpcam)(H2O)(SO4)] · 2H2O (2) and [Cu2(bpcam)2(H2O)2(SO4)] · H2O (3) [bpcam = bis(2-pyrimidylcarbonyl)amidate], whose structures have been determined by single-crystal X-ray diffraction studies. Copper(II) promotes the hydrolysis of tpymt in mild conditions yielding the bpcam group which is present in the structures of 1–3 as a tridentate ligand. The structure of 1 consists of mononuclear [Cu(bpcam)(H2O)2]+ cations, uncoordinated perchlorate anions and water of crystallization. Th…
Stabilities and Coordination Modes of α-Alaninephosphonic Acid in Copper(II) Heteroligand Complexes with Ethylenediamine, Diethylenetriamine or N,N,N…
2011
Solution equilibrium studies on Cu2+–L1–L2 ternary systems have been performed by pH-potentiometry, UV–Vis spectrophotometry and EPR methods (L1 corresponds to polyamines such as ethylenediamine (en), diethylenetriamine (dien), or N,N,N′,N′,N″-pentamethyldiethylenetriamine (Me5dien) and L2 represents 1-aminoethylphosphonic acid (α-alaninephosphonic acid)). The obtained results suggest the formation of heteroligand complexes with [Cu(L1)(α-Ala(P))] stoichiometry in all studied systems. Additionally, in the system with en the [Cu(en)(α-Ala(P))H−1]− species is formed in basic solution. Our spectroscopic results indicate tetragonal geometry for the [Cu(en)(α-Ala(P))] species, geometry slightly …
Documenting carved stones from 3D models. Part II - Ambient occlusion to reveal carved parts.
2021
10 pages; International audience; Revealing carved parts in rock art is of primary importance and remains a major challenge for archaeological documentation. Computational geometry applied to 3D imaging provides a unique opportunity to document rock art. This study evaluates five algorithms and derivatives used to compute ambient occlusion and sky visibility on 3D models of Mongolian stelae, also known as deer stones. By contrast with the previous companion work, models are processed directly in 3D, without preliminary projection. Volumetric obscurance gives the best results for the identification of carved figures. The effects of model resolution and parameters specific to ambient occlusio…