Reduction of operators with almost periodic symbols to operators overC *-Algebras on sections of associated bundles over a torus

A decomposition of any pseudodifferential operator (D) onR ⁿ with almost periodic symbol as 113-1 1 is obtained in the paper, where _A (D) is a pseudodifferential operator over a certainC ^*-algebraA acting on sections of a vector bundle over a torusT ⁿ whose fibre isA. The coincidence of spectra sp (D) = sp _A (D) is proved for all (D) either bounded or elliptic.     

Mild template synthesis of a copper(II)-containing macrocyclic compound with 4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9 in a gelatin-immobilized matrix

The complexing processes in the triple copper(II)–thiocarbohydrazide–propanone system taking place in a copper(II) hexacyanoferrate(II) gelatin-immobilized matrix in contact with aqueous-alkaline solutions (pH12), containing thiocarbohydrazide and propanone, have been studied. Template synthesis leading to a macrocyclic coordination compound with the tetradentate N,N,S,S-donor ligand, (4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9), occurs under these specific conditions when thiocarbohydrazide and propanone are the ligand synthons.     

Soft template synthesis in copper(II)–dithiooxamide–methanal,copper(II)–dithiooxamide–ethanal and copper(II)–dithiooxamide–propanone triple systems in a copper(II)hexacyanoferrate(II) gelatin-immobilized matrix

Novel complexing processes in the Cu^II–dithiooxamide–methanal, Cu^II–dithiooxamide–ethanal and Cu^II–dithiooxamide–propanone triple systems proceeding under specific conditions, to copper(II)hexacyanoferrate(II) gelatin-immobilized matrix systems in contact with aqueous-alkaline (pH 12) solutions containing dithiooxamide and methanal, ethanal or propanone, have been studied. It has been shown that template synthesis leading to the formation of macrocyclic coordination compounds (2,8-dithio-3,7-diaza-5-oxanonandithioamide-1,9)copper(II), (2,8-dithio-3,7-diaza-4,6-dimethyl-5-oxanonandithio-amide-1,9)copper(II) and (4,4,6-trimethyl-2,8-dithio-3,7-diazanonen-6-dithioamide-1,9)copper(II), respectively, takes place under such conditions. Dithiooxamide, methanal, ethanal and propanone act as ligand synthons in these processes.     

Synthesis of [1,3]dithiole and spiro[1,3]dithiole thiopyran derivatives of the [1,2]dithiolo[1,4]thiazine ring system

We report the synthesis of some new polysulfur-nitrogen heterocycles by cycloaddition reactions to readily available tricyclic condensed 1,2-dithiole-3-thiones. Thus, treatment of bis[1,2]dithiolopyrrole ketothione 1 with diacyl acetylenes gave the bis-aducts 2a-d. On the other hand, cycloaddition of bis[1,2]dithiolo[1,4]thiazine ketothione 3 with 1 equiv of acyl or diacyl acetylenes gave [1,3]dithiolylidenyl[1,2]dithiolo[1,4]thiazines 4a-f in fair to high yields. Catalysis by scandium triflate was used in the reactions that implied the less reactive dipolarophiles. Treatment of 3 with 2 equiv of DBA gave the bis-aduct 5a, and reaction of 4c with DMAD gave the mixed bis-adduct 5b. Cyclic voltammetry of selected examples showed irreversible processes that were influenced by the electrochemical activity of peripheral groups bonded to the heterocyclic system.     

Fine Structure of Meniscus of a Wetting Liquid

Equilibrium of a capillary meniscus near a wetting film on a solid in a gravitational field is considered. Unlike previous studies, the present study proves that the fine meniscus structure in a gravitational field is a universal feature—it takes place in a wide variety of problems. In the general case, the capillary meniscus is at a certain distance from the wetting film and does not intersect it. The relation for the minimum distance from the arbitrary meniscus to the solid generalizes the Derjaguin formula for a flat slit. An equation that optimally approximates the meniscus with due account of the contribution of the meniscus/film transition region is derived. A refined solution to the problem of a meniscus on a vertical plate is derived within the perturbation theory. Both gravity and nonuniformity of the vertical static film above a capillary–gravitational meniscus do not affect the minimum distance (the influence is less than 0.0001). A general method for solving sophisticated problems of capillary equilibrium in gravitational field is proposed.     

Variation–iteration method for one-dimensional two-electron systems

A quantum chemical study of the two low-lying quartet states of seven model compound I iron–porphyrin complexes with varying axial ligands has been carried out using the INDO method. The varying axial ligands included in this study are five that are models for those in the intact enzymes: imidazole and imidazolate (model peroxidase HRP and CCP), CH₃CONH₂ (Gln175 mutant of CCP), PhO^?1 (catalase), CH₃S^?1 (P450), and two that have been used in biomimetics of these enzymes: Cl^?1 (hemin) and PhS^?1 (model P450s). The purpose of these studies was to determine the role of the axial ligands in determining (i) the relative energies of the two nearly degenerate quartet electronic states of compound I, involved either as an a_1u or a_2u porphyrin π cation radical and (ii) the electron and spin distributions in the a_1u and a_2u radical cations of compound I. For most of the model complexes, including both HRP-I and CAT-I, a moderate effect of the axial ligand on the relative energy of these two states was observed and the a_1u radical cation was found to be the ground state. The energy order of these two radical cations, however, was reversed in the P450-I model complexes, indicating an association of the unique property of the Fe?O bond breaking with an a_2u radical cation. The symmetry-allowed overlap between the Fe?O and 3a_2u orbitals may lower the activation energy for the Fe?O bond cleavage in P450-I. However, the calculated electronic and spin properties, including the unpaired spin and net charge on the oxygen and the Fe?O bond overlap density, important determinants of the reactivity of this complex in the ligand–Fe?O region, are very similar for all complexes and in both cation states. © 1992 John Wiley & Sons, Inc.     

A stereoselective synthesis of asymmetrically substituted calix[4]arenecarbamates

Calix[4]arenes bearing a methoxy and an R or S α-phenylethylacetamido group at the narrow rim of macrocycles are stereoselectively acylated with 1 equiv of trichloroacetyl isocyanate to give chiral asymmetrically substituted calix[4]arenecarbamates in preparative yields and high diastereomeric excess.     

Addition of nitriles to alkaline earth metal complexes of 1,2-bis[(phenyl)imino]acenaphthenes

Compounds [Sr(dpp-bian)(thf)4] (2), [Ba(dpp-bian)(dme)2.5] (3) and [Mg(dtb-bian)(thf)2] (4) (dpp-bian = 1,2-bis[(2,6-diisopropylphenyl)imino]acenaphthene; dtb-bian = 1,2-bis[(2,5-di-tert-butylphenyl)imino]acenaphthene) were prepared by reduction of dpp-bian and dtb-bian with an excess of metallic Mg, Sr, or Ba in THF or DME. Reactions of [Mg(dpp-bian)(thf)3], 3, and 4 with diphenylacetonitrile gave keteniminates [Mg(dpp-bianH)(NCCPh2)(thf)2] (5), [Mg(dtb-bianH)(NCCPh2)(thf)2] (6), and [Ba(dpp-bianH)(NCCPh2)(dme)2] (7), respectively. The reaction of 2 with CH3C[triple chemical bond]N in THF gave [{Sr(dpp-bianH)[N(H)C(CH3)C(H)CN](thf)}2] (8). The compounds 2, 3, 5-8 were characterized by elemental analysis, and IR and NMR spectroscopy. Molecular structures of 2, 3, 7, and 8 were determined by single-crystal X-ray diffraction. In contrast to reactions of alkali-metal reagents, magnesium amides, or yttriumalkyls with alpha-H acidic nitriles, which are accompanied by an amine or an alkane elimination, the reactions of [Mg(dpp-bian)(thf)3] (1), 2, 3, and 4 with such nitriles proceeded with formation of Mg, Sr, and Ba keteniminates and simultaneous protonation of one nitrogen atom of the bian ligand. The NMR spectroscopic data obtained for complex 5 indicated that in solution the amino hydrogen atom underwent the fast (on the NMR timescale) shuttle transfer between both nitrogen atoms of the dpp-bianH ligand.     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.