944 resultados para 4-DIMENSIONAL RIEMANNIAN MANIFOLD
Resumo:
In the structure of the title compound C8H12NO+ C7H5O6S- . H2O, from the reaction of 2-(4-aminophenyl)ethanol with 5-sulfosalicylic acid, the cations form head-to-tail hydrogen-bonded chains through C1/1(9) anilinium N+-H...O(hydroxyl} interactions while the anions also form similar but C1/1(8)-linked chains through carboxylic acid O-..O(sulfonate) interactions. The chains inter-associate through a number of N-H...O and O-H...O bridging interactions giving a two-dimensional array in the ab plane.
Resumo:
A complete series of cross-sectional computed tomography (CT) scans were obtained of a mummy of an Egyptian priestess, Tjenmutengebtiu, (Jeni), who lived in the twenty-second Dynasty (c. 945-715 BC). The purpose of this joint British Museum and St. Thomas’ Hospital project was effectively to ‘unwrap’ a mummy using cross-sectional X-rays. Jeni is encased in a beautifully decorated anthropomorphic cartonnage coffin. The head and neck were scanned with 2mm slices, the teeth with 1mm slices and the rest of the body with 4 mm slices, a 512 x 512 matrix was used. The 2D CT images, and 3D surface reconstruction’s, demonstrate many features of the embalming techniques and funerary customs of the XXII Dynasty. The presence of cloth protruding from the nasal cavities into the otherwise empty cranial cavity indicates that the brain was extracted via the nose. The remains of the heart can be seen as well as four organ packs corresponding to the mummified and repackaged lungs, intestines, stomach and liver. Each of the organ packs encloses a wax figurine representing one of the four sons of Horus. The teeth are in very good condition with little signs of wear, which, considering the gritty diet of the Egyptians, indicates that Jeni must have been very young when she died. A young age of death is also suggested by analysis of the shape of the molar teeth. The body is generally in very good condition demonstrating the consummate skill of the twenty-second Dynasty embalmers.
ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation
Resumo:
In the structure of the 1:1 proton-transfer compound of isopropylamine with 4,5-dichlorophthalic acid, C3H10N+·C8H3Cl2O4-, the three cation H-atom donors associate with three separate carboxyl O-atom anion acceptors, giving conjoint cyclic R44(12), R44(16) hydrogen-bonding cation-anion interactions in a one-dimensional ribbon structure. In the anions, the carboxyl groups lie slightly out of the plane of the benzene ring [maximum deviations = 0.439 (1) for a carboxylic acid O atom and 0.433 (1) Å for a carboxylate O atom]. However, the syn-related proton of the carboxylic acid group forms the common short intramolecular O-HOcarboxyl hydrogen bond.
Resumo:
In the structure of the title compound, C2H10N22+·C8H2Cl2O42-, the dications and dianions form hydrogen-bonded ribbon substructures which enclose conjoint cyclic R21(7), R12(7) and R42(8) associations and extend down the c-axis direction. These ribbons inter-associate down b, giving a two-dimensional sheet structure. In the dianions, one of the carboxylate groups is essentially coplanar with the benzene ring, while the other is normal to it [C-C-C-O torsion angles = 177.67 (12) and 81.94 (17)°, respectively].
Resumo:
The unusual (1:1) complex ‘adduct’ salt of copper(II) with 4,5-dichlorophthalic acid (H2DCPA), having formula [Cu(H2O)4(C8H3Cl2O4) (C8H4Cl2O4)] . (C8H3Cl2O4) has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P21/c, with Z = 4 in a cell with dimensions a = 20.1376(7), b =12.8408(4) c = 12.1910(4) Å, β = 105.509(4)o. The complex is based on discrete tetragonally distorted octahedral [CuO6] coordination centres with the four water ligands occupying the square planar sites [Cu-O, 1.962(4)-1.987(4) Å] and the monodentate carboxyl-O donors of two DCPA ligand species in the axial sites. The first of these bonds [Cu-O, 2.341(4) Å] is with an oxygen of a HDCPA monoanion, the second with an oxygen of a H2DCPA acid species [Cu-O, 2.418(4) Å]. The un-coordinated ‘adduct’ molecule is a HDCPA counter anion which is strongly hydrogen-bonded to the coordinated H2DCPA ligand [O… O, 2.503(6) Å] while a number of peripheral intra- and intermolecular hydrogen-bonding interactions give a two-dimensional network structure.
Resumo:
Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.
Resumo:
The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.
Resumo:
The 1:1 proton-transfer compound of the potent substituted amphetamine hallucinogen (R)-1-(8-bromobenzo[1,2-b; 4,5-b']difuran-4-yl)-2-aminopropane (common trivial name 'bromodragonfly') with 3,5-dinitrosalicylic acid, 1-(8-bromobenzo[1,2-b;4,5-b']difuran-4-yl)-2-mmoniopropane 2-carboxy-4,6-dinitrophenolate, C13H13BrNO2+ C7H3N2O7- forms hydrogen-bonded cation-anion chain substructures comprising undulating head-to-tail anion chains formed through C(8) carboxyl O-H...O(nitro) associations and incorporating the aminium groups of the cations. The intra-chain cation-anion hydrogen-bonding associations feature proximal cyclic R33(8) interactions involving both a N+-H...O(phenolate) and the carboxyl O--H...O(nitro)associations. Also present are aromatic pi-pi ring interactions [minimum ring centroid separation, 3.566(2)A; inter-plane dihedral angle, 5.13(1)deg]. A lateral hydrogen-bonding interaction between the third aminium proton and a carboxyl O acceptor link the chain substructures giving a two-dimensional sheet structure. This determination represents the first of any form of this compound and confirms that it has the (R) absolute configuration. The atypical crystal stability is attributed both to the hydrogen-bonded chain substructures provided by the anions, which accommodate the aminium proton-donor groups of the cations and give cross-linking, and to the presence of cation--anion aromatic ring pi-pi interactions.
Resumo:
In the structure of the title compound, the salt 2(C12H10N3O4+) (C12H8O6S2)2- . 3H2O, determined at 173 K, the biphenyl-4,4'-disulfonate dianions lie across crystallographic inversion centres with the sulfonate groups interacting head-to-head through centrosymmetric cyclic bis(water)-bridged hydrogen-bonding associations [graph set R4/4(11)], forming chain structures. The 2-(2,4-dinitrobenzyl)pyridinium cations are linked to these chains through N+-H...O(water) hydrogen bonds and a two-dimensional network structure is formed through water bridges between sulfonate and 2-nitro O atoms, while the structure also has weak cation--anion pi-pi aromatic ring interactions [minimum ring centroid separation 3.8441(13)A].
Resumo:
In the structure of the 1:1 proton-transfer compound of 4-methylpyridine (\g-picoline) with 4,5-dichlorophthalic acid, C6H8N+ C8H3Cl2O4- . H2O, determined at 200 K, the 4,5-dichlorophthalate anions are bridged by the water molecule through O--H...O~carboxyl~ hydrogen bonds, giving zig-zag chains which extend along the c axial direction of the unit cell. The 4-methylpyridine cations are linked to the chains through single N--H...O~water~ hydrogen bonds and occupy the voids within the chains in the one-dimensional structure. The anions have the common 'planar' conformation with the short intramolecular O--H...O(carboxyl) hydrogen bond.
Resumo:
The structures of bis(guanidinium)rac-trans-cyclohexane-1,2-dicarboxylate, 2(CH6N3+) C8H10O4- (I), guanidinium 3-carboxybenzoate monohydrate CH6N3+ C8H5O4- . H2O (II) and bis(guanidinium) benzene-1,4-dicarboxylate trihydrate, 2(CH6N3+) C8H4O4^2- . 3H2O (III) have been determined and the hydrogen bonding in each examined. All three compounds form three-dimensional hydrogen-bonded framework structures. In anhydrous (I), both guanidinium cations give classic cyclic R2/2(8) N--H...O,O'(carboxyl) and asymmetric cyclic R1/2(6) hydrogen-bonding interactions while one cation gives an unusual enlarged cyclic interaction with O acceptors of separate ortho-related carboxyl groups [graph set R2/2(11)]. Cations and anions also associate across inversion centres giving cyclic R2/4(8) motifs. In the 1:1 guanidinium salt (II), the cation gives two separate cyclic R1/2(6) interactions, one with a carboxyl O-acceptor, the other with the water molecule of solvation. The structure is unusual in that both carboxyl groups give short inter-anion O...H...O contacts, one across a crystallographic inversion centre [2.483(2)\%A], the other about a two-fold axis of rotation [2.462(2)\%A] with a half-occupancy hydrogen delocalized on the symmetry element in each. The water molecule links the cation--anion ribbon structures into a three-dimensional framework. In (III), the repeating molecular unit comprises a benzene-1,4-dicarboxylate dianion which lies across a crystallographic inversion centre, two guanidinium cations and two water molecules of solvation (each set related by two-fold rotational symmetry), and a single water molecule which lies on a two-fold axis. Each guanidinium cation gives three types of cyclic interactions with the dianions: one R^1^~2~(6), the others R2/3(8) and R3/3(10) (both of these involving the water molecules), giving a three-dimensional structure through bridges down the b cell direction. The water molecule at the general site also forms an unusual cyclic R2/2(4) homodimeric association across an inversion centre [O--H...O, 2.875(2)\%A]. The work described here provides further examples of the common cyclic guanidinium cation...carboxylate anion hydrogen-bonding associations as well as featuring other less common cyclic motifs.
Resumo:
In the title isonipecotamide salt 2C6H13N2O+.C12H8O6S22-,the asymmetric unit comprises one biphenyl-4,4'-disulfonate dianion which lies across a crystallographic inversion centre and another in a general position [dihedral angle between the two phenyl rings is 37.1(1)deg], together with three isonipecotamide cations. Two of these cations give a cyclic homomeric amide-amide dimer interaction [graph set R2/2(8)],the other giving a similar dimeric interaction but across an inversion centre, both dimers then forming lateral cyclic R2/4(8) pyrimidinium N-H...O interactions. These units are linked longitudinally to the sulfonate groups of the dianions through piperidinium N-H...O hydrogen bonds, giving a three-dimensional framework structure.
Resumo:
In the structure of the title compound, C6H13N2O+ C2H3O2- . H2O, the amide H atoms of the cations form centrosymetric cyclic hydrogen-bonding associations incorporating two water molecules [graph set R^2^~4~(8)], which are conjoint with cyclic water-bridged amide-amide associations [R^4^~4~(12)] and larger R4/4(20) associations involving the water molecule and the acetate anions, which bridge through the piperidinium H donors, giving an overall three-dimensional framework structure.