A metric on the manifold of immersions and its Riemannian curvature

E. Binz [1] considered two canonical Riemannian metrics on the space of embeddings of a closed (n–1) dimensional manifold into ⁿ , and computed the geodesic sprays. Here we consider the space of immersions Imm (M, N) whereM is without boundary, and we compute the covariant derivative (in the form of its connector) and the Riemannian curvature of one of these metrics, the non trivial one. The setting is close to that used byP. Michor [2], and we refer the reader to this paper for notation.     

Fluorescent properties of oligonucleotide-conjugated thiazole orange probes

The fluorescence properties of thiazole orange, linked via a (1) hydrophobic alkyl or a (2) hydrophilic ethylene glycol chain to the central internucleotidic phosphate group of a pentadeca-2'-deoxyriboadenylate (dA15), are evaluated. Linkage at the phosphate group yields two stereoisomers, S-isomer of the phosphorus chiral center (Sp) and R-isomer of the phosphorus chiral center (Rp); these are studied separately. The character of the linkage chain and the chirality of the internucleotidic phosphate linkage site influence the fluorescent properties of these thiazole orange-oligonucleotide conjugates (TO-probes). Quantum yields of fluorescence (phifl) of between 0.04 and 0.07 were determined for the single-stranded conjugates. The fluorescence yield increased by up to five times upon hybridization with the complementary sequence (d5'[CACT15CAC3']); (phifl values of between 0.06-0.35 were determined for the double-stranded conjugates. The phifl value (0.17) of thiazole orange, 1-(N,N'-trimethylaminopropyl)-4-[3-methyl-2,3-dihydro-(benzo-1,3-thiazole)-2-methylidene]-quinolinium iodide (TO-Pro 1) in the presence of the oligonucleotide duplex (TO-Pro 1: dA15.d5'[CACT15CAC3'] (1:1)) is much less than that for some of the hybrids of the conjugates. Our studies, using steady-state and time-resolved fluorescence experiments, show that a number of discrete fluorescent association species between the thiazole orange and the helix are formed. Time-resolved studies on the four double-stranded TO-probes revealed that the fluorescent oligonucleotide-thiazole orange complexes are common, only the distribution of the species varies with the character of the chain and the chirality at the internucleotidic phosphate site. Those TO-probes in which the isomeric structure of the phosphate-chain linkage is Rp, and therefore such that the fluorophore is directed toward the minor groove, have higher phifl values than the Sp isomer. Of the systems studied, thiazole orange linked by an alkyl chain to the internucleotidic phosphate (Rp isomer) has the highest phifl and the greatest fraction of the longest-lived fluorescent thiazole orange species (in the hybrid form).     

Synthesis,crystal structure,magnetism, and absorption spectra of A2UX5 Type Halides (A = K,Rb; X = Cl,Br, I)

The ternary uranium(III) halides A₂UX₅ (A = K, Rb; X = Cl, Br, I) have been prepared from the binary components AX and UX₃ in sealed tantalum containers. According to their Guinier X-ray powder patterns, they all crystallize with the K₂PrCl₅/Y₂HfS₅ type of structure. Lattice constants for ambient temperature are reported. Single-crystal structure refinemens were undertaken for K₂UI₅ and Rb₂UCl₅. Magnetic susceptibility data were recorded with a SQUID magnetometer from liquid helium to room temperature. One-dimensional (intrachain) and three-dimensional antiferromagnetic ordering occur at low temperatures dependent upon the U³⁺? U³⁺ distance. Absorption spectra were recorded between 4 000 and 28 000 cm^?1. They show f—f transitions typical for U³⁺ and, depending on the halide, very strong f—d transitions above 14 000 to 15 000 cm^?1, respectively.     

Die Tieftemperatur-Synthese von Oxidhalogeniden,YOX (X = Cl,Br, I), als Quelle der Verunreinigung von Yttriumtrihalogeniden,YX3, bei der Gewinnung nach der Ammoniumhalogenid-Methode. Die Analogie von YOCl und YSCl

Low-Temperature Synthesis of Oxyhalides, YOX (X = Cl, Br, I), as the Source of Impurity in the Preparation of Trihalides, YX₃, via the Ammonium Halide Route. Analogy of YOCl and YSCl Ammonium halides, NH₄X (X = Cl, Br, I), react with Y₂O₃ and Y₂S₃, respectively, at temperatures as low as 230=C (X = Cl), 280=C (Br), and 360=C (I) (molar ratio 12:1) to yield (NH₄)₃YX₆, NH₃, and H₂O (H₂S). The choice of smaller ratios than 12:1 (for example 2:1) results in the formation of oxyhalides, YOX, via the reaction of (NH₄)₃YX₆ with surplus Y₂O₃. This reaction is therefore the actual source of impurity of rare-earth trihalides in their preparation via the ammonium halide routes.     

Ternäre Halogenide der Seltenen Erden vom Typ A2MX5 (A = K,In, NH4, Rb,Cs; X = Cl,Br, I)

Ternary Rare-Earth Halides of the A₂MX₅ Type (A = K, In, NH₄, Rb, Cs; X = Cl, Br, I) Ternary rare-earth (=M) chlorides, bromides, and iodides In₂MCl₅, (NH₄)₂MCl₅, Rb₂MCl₅, Cs₂MCl₅, CsRbMCl₅, K₂MBr₅, Rb₂MBr₅, K₂MI₅, and Rb₂MI₅ have been synthesized. Single crystals of In₂PrCl₅, Rb₂PrCl₅, K₂PrBr₅, and K₂PrI₅ were grown and the structures refined. The other halides were characterized by x-ray powder patterns. They are isotypic either with K₂PrCl₅(orthorhombic, Pnma, Z = 4, hexagonal arrangement of chains of edge-connected polyhedra [PrX₇]) or with Cs₂DyCl₅ (orthorhombic, Pbnm, Z = 4, hexagonal arrangement of cis-corner-connected octahedra [DyCl₆]) which may be discriminated in structure field diagrams. The thermal expansion was investigated für Cs₂LuCl₅ and Rb₂PrX₅ (X = Cl, Br, I).     

Thermal transitions of DODAB vesicular dispersions

Two endothermic transitions, at 36°C and 44°C, were observed with differential scanning calorimetry (DSC) upon heating dioctadecyldimethylammonium bromide vesicle dispersions that were equilibrated below 15°C while in samples kept at 25°C there was only the transition at 44°C, which was shown to be the gel to liquid–crystalline transition by ¹H-NMR measurements. The transition at 36°C was reversed in an exothermic transition around 13°C upon cooling. The slowness of this transition at ambient temperatures suggests that the presence of the transition at 36°C in a DSC upscan depends strongly on the sample history.     

Kristallstrukturen zweier Modifikationen von In5Mo18O28 und deren Zwillingsbildung

Crystal Structures of Two Forms of In₅Mo₁₈O₂₈ and Twinning In₅Mo₁₈O₂₈ is prepared from In, Mo and MoO₂ at 1 150°C in an evacuated quartz glass ampoule. X-ray investigations on single crystals show monoclinic symmetry (a = 1 323.13(9), b = 951.88(10), c = 989.48(8) pm, β = 100.976(4)°, space group P 2₁/c (No. 14)) for form 1 . The second form ( 2 ) crystallizes in the orthorhombic system (space group Pmcn (No. 62), a = 2 596.6(5), b = 952.0(2), c = 989.6(2) pm). Twinning and charge balances are discussed.     

Trimethylsilylverbindungen der Vb-Elemente. VII. Die Kristallstrukturen von Lithium-bis(trimethylsilyl)bismutid · DME und Tetrakis(trimethylsilyl)dibismutan sowie Bemerkungen zur Kristallstruktur des Bis(4-methoxyphenyl)ditellans

Trimethylsilyl Derivatives of Vb Elements. VII. Crystal Structures of Lithium Bis(trimethylsilyl)bismuthide · DME and of Tetrakis(trimethylsilyl)dibismuthane as well as Some Comments on the Crystal Structure of Bis(4-methoxyphenyl)ditellane Colourless lithium bis(trimethylsilyl)bismuthide · DME

1 1,2-Dimethoxyethan (DME); Tetrahydrofuran (THF)

1 and green, metallic lustrous tetrakis(trimethylsilyl)dibismuthane 2 crystallize isotopic to their antimony homologues [1, 2]. As it is shown by crystal structure determinations { 1 : ?90°C; I 4 2d; a = 1017,3(4); c = 3738,0(26) pm; Z = 8; R _w = 0,065; 2 : + 20°C; P2 ₁ /c; a = 680,9(4); b = 1704,8(13); c = 1197,9 (10) pm; β = 119,46(6)°; Z = 2; R _w = 0,084} both compounds form chains which in the case of bismuthide 1 are built up as screws of alternating bismuth and lithium atoms; bonding further to two trimethylsilyl groups or to the chelating DME ligand both atoms gain coordination number 4 {Li? Bi 292(3); Bi? Si 263.3(14) pm; Bi? Li? Bi 132(1); Li? Bi? Li 148(1); φ(Li? Bi? Li? Bi) 83°}. In the case of dibismuthane 2 the centrosymmetric molecules are strung, their Bi-Bi groups forming nearly linear zigzag chains with shortened intermolecular contact distances {Bi-Bi 303.5(3); Bi …? Bi 380.4(3); Bi? Si 268 pm; Bi? Bi …? Bi 169; Bi? Bi? Si 97.4(5) and 92.0(5)°}. Structure and properties of 2 are compared with those of similar compounds; the crystal structure of brown, green metallic lustrous bis(4-methoxyphenyl)ditellane 5 already published by Ludlow and McCarthy[3] is reinvestigated with respect to very short intermolecular Te…?Te contacts.     

Das Indiumsesquichlorid,In2Cl3: ein pseudobinäres,gemischtvalentes Indium(I)-hexachloroindat(III)

Indium Sesquichloride, In₂Cl₃: a Pseudobinary, Mixed-valence Indium(I) Hexachloroindate(III) Colorless In₂Cl₃, obtained by reduction of InCl₃ with metallic In, according to In[In^IIICl₆] a pseudobinary, mixed-valence indium(I) hexachloroindate(III), crystallizes orthorhombic (Pnma, Z = 32) with a = 1261.4(3), b = 2523.8(5), c = 1456.2(2) pm (Guinier-Simon data), V_m(In₂Cl₃) = 87.3 cm³ × mol^?1. In^III occupies octahedral holes separated from each other (d?(In^III? Cl) = 251 pm). Coordination numbers of 7 to 11 are observed for In^I (d?(In^I? Cl) = 329–359 pm). In₂Cl₃ is isotypic with α-Tl₂Cl₃.     

(C2H10N2)[BPO4F2] — Structural Relations between [BPO4F2]2— and [Si2O6]4—

(C₂H₁₀N₂)[BPO₄F₂] — Strukturbeziehungen zwischen [BPO₄F₂]^2— und [Si₂O₆]^4— Colourless crystals of (C₂H₁₀N₂)[BPO₄F₂] were prepared from mixture of ethylendiamine, H₃BO₃, BF₃ · C₂H₅NH₂, H₃PO₄ and HCl under mild hydrothermal conditions (220 °C). The crystal structure was determined by single crystal methods (triclinic, P1¯ (no. 2), a = 451.85(5) pm, b = 710.20(8) pm, c = 1210.2(2) pm, α = 86.08(1)°, β = 88.52(2)°, γ = 71.74(1)°, Z = 2) and contains infinite tetrahedral zweier‐single‐chains {[BPO₄F₂]^2—} which are isoelectronic (48e^—) with the polyanions {[Si₂O₆]^4—} of the pyroxene family.