The hyperbolic n-space as a graph in Euclidean (6n−6)-space

We construct for each n2 an isometric C-imbedding HⁿE^6n–6 of the n-dim. hyperbolic space into the Euclidean space E^6n–6 whose image is the graph of a C-map RⁿR^5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2).     

Determination of aromatic sulfonic acids in industrial waste water by ion-pair chromatography

A method for the identification and quantification of aromatic sulfonic acids in industrial waste water has been developed. The preparation of the samples comprises a clean-up step and an enrichment step, utilizing i) reversed-phase extraction and ii) ion-pair solid phase extraction. The aromatic sulfonic acids are separated by ion-pair chromatography with diode-array detection. An advantage of the developed ion-pair chromatographic method is the separation of linear alkylbenzenesulfonic acids (LAS), lignosulfonic acids and aromatic sulfonic acids in one chromatographic run. Also described is an optimized clean-up procedure for collected fractions of a preparative chromatographic run to identify monosulfonic acids with GC/MS after methylation. The detection limits for aromatic sulfonic acids in industrial waste waters are at the g/l level.     

Determination of the quaternary compound ciclotropium in human biological material after hydrolysis and derivatization with the fluorophor flunoxaprofen chloride

The quantitative determination of the quaternary spasmolytic compound ciclotropium and its metabolite N-isopropyltropinium is described for human plasma and urine. The analytical procedure consists of ion-pair extraction from biological material, alkaline hydrolysis, subsequent derivatization with the fluorophor flunoxaprofen chloride and separation by high-performance liquid chromatography on a reversed-phase column with fluorimetric monitoring. The detection limits of 0.5 ng/ml in plasma and 10 ng/ml in urine at signal-to-noise ratios higher than 3 permit the determination of pharmacokinetic parameters after therapeutic doses.     

Extension of conjugation leading to bathochromic or hypsochromic effects in OPV series

Four OPV series 1-4 (a-d) with a terminal dialkylamino group as electron donor were prepared by Wittig-Horner reactions. To study the influence of the push-pull effect on the long-wavelength absorption, three of the four series contained terminal acceptor groups (CN, CHO, NO(2)). The length of the chromophores strongly affects the intramolecular charge transfer (ICT)-an effect which superimposes upon the extension of the conjugation. Increasing numbers n of repeat units cause an overall bathochromic shift for the purely donor-substituted series 1 a-4 a and the series 1 b-4 b with CN as weak acceptor. The two effects annihilate each other in the series 1 c-4 c with terminal CHO groups, so that the absorption maxima are almost independent of the length of the chromophore. A hypsochromic shift is observed for the series 1 d-4 d, which contains the strong acceptor group NO(2). This anomaly disappears on protonation of the dialkylamino group because the push-pull effect disappears in the ammonium salts. The results can be explained by semiempirical quantum mechanics (AM1, INDO/S). The HOMO-LUMO transition, which is mainly responsible for the ICT, becomes less important in the electron transitions S(0)-->S(1) when the distance between donor and acceptor is increased. The commonly used VB model, which contains an electroneutral and a zwitterionic resonance structure, is contrasted with a MO model with dipole segments at both ends of the OPV chains. The latter model turned out to be more appropriate-at least for donor-acceptor-substituted OPVs with n >/= 2.     

Die molekül- und kristallstruktur von thallium-tris(bistrimethylsilylamin), Tl[N(SiMe3)2]3

The molecular and crystal structure of tris(bistrimethylsilylamin)thallium was determined by means of single-crystal X-ray spectroscopy: in the space group P$\text{3}$1c with a = 16.447(7), c = 8.456(7) Å; and D_c = 1.149 g cm^?3 two molecules are located in the unit cell. The compound is isomorphous to the analogues Fe[N(SiMe₃)₂]₃ or Al[N(SiMe₃)₂]₃, respectively, which show a propellar-twist of the Si₂N-groups versus the plane of the metal atom and the three nitrogen-atoms: Tl(N)₃/Si₂N 49.1°; SiNSi 122.6°; NSiC 111.8°; CSiC 107.1°; TlN 2.089 Å;; SiN 1.738 Å;; $\text{SiC}$ 1.889 Å;.     

Kristallstruktur und Pseudosymmetrie einer neuen Modifikation von Kaliumhexachloroniobat(V), KNbCl6. Anmerkungen zur kubischen Phase

Crystal Structure and Pseudosymmetry of a New Modification of Potassium Hexachloroniobate(V), KNbCl₆. Comments on the Cubic Phase Long needles of KNbCl₆ – invariably twinned around [100] – are obtained if the material is crystallized from SOCl₂ solution. The structure has been determined from X-ray data collected with a single-crystal diffractometer at room temperature [space group P2₁/n, Z = 16, a = 6.894(1), b = 22.073(4), c = 23.337(3) Å, β = 91.00(1)°, R = 0.032 for 2 909 unique reflexions, 290 structural parameters]. Distorted NbCl₆^? octahedra and ?interstitial’? K⁺ ions are found to form similar arrangements, each of them corresponding to a closest packing of spheres with the layer sequence ACAB (stacking symbol hc). The resulting asymmetry in coordination by potassium is coupled with a strong off-centre displacement of the Nb atoms in any of the four independent chlorine polyhedra (0.14 Å on average). A pronounced pseudosymmetry accounts for the twinning. Since P2₁/m2₁/n2₁/b (no. 62) is already a good approximation of the real structure, only one formal step of symmetry reduction (index t2) is needed to create both, the observed twin law and the actual space group P1 2₁/n1. Above 180°C a reconstructive phase transition leads to the ‘face-centred cubic’ modification with ～ 10% lower density.     

Synthesis and Crystal Structure of [C10N2H10]2[P2Mo5O21(OH)2]·2H2O

The crystal structure of [C₁₀N₂H₁₀]₂[P₂Mo₅O₂₁(OH)₂] · 2H₂O, contains the heteropolyanion, [P₂Mo₅O₂₁(OH)₂]^4—, together with diprotonated 4, 4′‐bipyridine. The heteropolyanion is built up from five MoO₆ octahedra sharing four common edges and one common corner, capped by two PO₃(OH) tetrahedra. The structure is stabilized by hydrogen bonds involving the hydrogen atoms of the 4, 4′‐bipyridine, water molecules and the oxygen atoms of the pentamolybdatobisphosphate. This is the first example that this kind of cluster could be isolated in the presence of a poly‐functional aromatic molecule ion. Crystal data: triclinic, P1¯ (No. 2), a = 9.983(2)Å, b = 11.269(2)Å, c = 17.604(4)Å, α = 73.50(3)°, β = 84.07(3)°, γ = 67.96(3)°; V = 1760.0(6)ų; Z = 2; R₁ = 0.037 and wR₂ = 0.081, for 9138 reflections [I > 2σ(I)].     

Structural Patterns and Dimensionality in Magnesium Borophosphates: The Crystal Structures of Mg2(H2O)[BP3O9(OH)4] and Mg(H2O)2[B2P2O8(OH)2]·H2O

Hydrothermal investigations in the system MgO/B₂O₃/P₂O₅(/H₂O) yielded two new magnesium borophosphates, Mg₂(H₂O)[BP₃O₉(OH)₄] and Mg(H₂O)₂[B₂P₂O₈(OH)₂]·H₂O. The crystal structures were solved by means of single crystal X‐ray diffraction. While the acentric crystal structure of Mg₂(H₂O)[BP₃O₉(OH)₄] (orthorhombic, P2₁2₁2₁ (No. 19), a = 709.44(5) pm, b = 859.70(4) pm, c = 1635.1(1) pm, V = 997.3(3) × 10⁶ pm³, Z = 4) contains 1D infinite chains of magnesium coordination octahedra interconnected by a borophosphate tetramer, Mg(H₂O)₂[B₂P₂O₈(OH)₂]·H₂O (monoclinic, P2₁/c (No. 14), a = 776.04(5) pm, b = 1464.26(9) pm, c = 824.10(4) pm, β = 90.25(1)°, V = 936.44(9) × 10⁶ pm³,Z = 4) represents the first layered borophosphate with 6³ net topology. The structures are discussed and classified in terms of structural systematics.