Gao’s conjecture on zerosum sequences

In this paper, we shall address three closely-related conjectures due to van Emde Boas, W D Gao and Kemnitz on zero-sum problems on Z_p ⊗ Z_p. We prove a number of results including a proof of the conjecture of Gao for the primep = 7 (Theorem 3.1). The conjecture of Kemnitz is also proved (Propositions 4.6, 4.9, 4.10) for many classes of sequences.     

Organic-inorganic hybrid compounds of Li with bisimidazole derivatives: Li ion binding study and topochemical properties

The imidazole-based ligands, bis(imidazol-1-yl)methane (Bizm, 1a) and (pyrenyl)bis(imidazol-1-yl) methane (Pbizm,2a) were prepared. With LiClO4, these two compounds formed two novel organic-inorganic hybrid materials: a 3D network polymer Li(Bizm).ClO4 (1b) and a 1D chain polymer Li(Pbizm)2.ClO4 (2b). The intriguing topological and physiochemical characteristics of 1b and 2b are reported on the basis of the X-ray single-crystal structure analysis and Li ion binding studies.     

Characterization of a new decahydropyridoquinoline from Indigofera longeracemosa Boiv. ex Baill. (Fabaceae)

Repeated silica gel chromatography of the dichloromethane extract of air-dried stems of Indigofera longeracemosa followed by reverse-phase HPLC separation yielded a new decahydropyridoquinoline, rel-(3S, 5R, 6S, SR, 8aR, 12aR)-8-acetoxy-6-butyl-3-isothiocyanatodecahydropyrido (2,1) quinoline.     

Semiconducting SnO<Subscript>2</Subscript>-TiO<Subscript>2</Subscript> (S-T) composites for detection of SO<Subscript>2</Subscript> gas

SnO₂-TiO₂ (S-T) composites with different molar ratios were prepared by mechanical mixing followed by sintering at 700 °C for 4 h in air. The structural and microstructural properties of the composites were investigated using powder X-ray diffraction (PXRD) and scanning electron microscopy (SEM). S-T composites were investigated by introducing SO₂ to test their chemical stability using PXRD and SEM coupled with energy dispersive X-ray (EDX) analysis. The sensing performance was measured at different temperatures using various SO₂ concentrations (10–100 ppm). A composite comprising 25 mol% of SnO₂ and 75 mol% TiO₂ (S25-T75) exhibited the highest sensitivity comparing to other S-T composites studied under the presently investigated conditions. t ₉₀ (90 % of response time) was found to be ～5 min for thick pellet (~2 mm in thickness). SO₂ sensing mechanism has been explained through the band structure model.     

Mixed ligand complexes of ruthenium(II) containing α,β-unsaturated-β-ketoaminesand their antibacterial activity

Hexacoordinated Ru^II complexes of the [RuX(CO)(PPh₃)(B)(LL)] type [X = Cl; B = PPh₃, pyridine (py), piperidine (pip) or morpholine (morph); LL = ,-unsaturated--ketoaminate] have been synthesised by reacting [RuHCl(CO)(PPh₃)(B)] (B = PPh₃, py, pip or morph) with the appropriate -ketoamine in a 1:1 molar ratio. The replacement of hydride ion and the triphenylphosphine group by a bidentate chelating ligand from the starting compounds occurs. The complexes were characterised by elemental analyses and spectral (i.r., electronic, ¹H- and ³¹P-n.m.r.) data. Antibacterial activity were also tested for in these new complexes.     

Phase transitions in the SrSnO3-SrFeO3 solid solutions: X-ray diffraction and Mössbauer studies

SrSn_1−xFe_xO_y (0?x?1) oxides were prepared by conventional solid-state reaction in air using high-purity (?99%) SrCO₃, SnO₂ and Fe(C₂O)₂·2H₂O at elevated temperatures of 1300°C for 24 h and furnace cooled. Samples obtained from 1300°C were annealed at 620°C for 2 days and quenched in liquid nitrogen (LN). Powder XRD analysis by Rietveld refinement and Fe Mössbauer spectroscopy measurements were employed to characterize synthesized perovskites. Samples obtained from furnace cooled and LN quenched undergo two compositionally driven phase transitions, which are supposed to be of second order. The x=0-0.3 members crystallize in orthorhombic parent SrSnO₃ structure (Space group Pbnm), whereas samples x=0.4-0.9 have a simple cubic perovskite cell and end-member SrFeO_2.74 composition crystallize orthorhombic structure (Space group Cmmm). The composition of the first phase transition (x≈0.3) is slightly shifted to higher x with decreasing annealing temperature. Mössbauer data show that the Fe⁴⁺/Fe^tot ratio is depending on composition under constant synthesis conditions. The phase compositions have been discussed in terms of ternary solid solution of compounds SrSnO₃-SrFeO_2.74-SrFeO_2.5 superior to a simple binary solid solution (SrSnO₃-SrFeO₃).     

On Steinhaus sets

We give a common proof of several results on Steinhaus sets in for d2 including the fact that a Steinhaus set in must be disconnected.     

Investigations of praseodymium oxide electrodes in lithium concentration cells

Praseodymium oxide is one of the group of binary oxides that show a wide range of stoichiometry, but in which the deviation from the ideal stoichiometry is not continuous, as is expected from the classical model of randomly distributed isolated point defects. Instead, there is a number of phases of unique structures and stoichiometries with no appreciable concentrations of point defects, and thus essentially no compositional width. These structures are closely related to each other, and to a simple parent structure. In the case of praseodymium oxide this is the fluorite structure. Transitions between these phases upon heating and cooling, as well as upon changes in the oxygen activity of the environment, occur very rapidly, indicating unusually high oxygen mobility. The equilibrium phase at ambient temperature in air is not PrO₂, but Pr₆O₁₁. These phases have been shown to have cation sublattices essentially identical to that of fluorite-type PrO₂. The stoichiometric changes are accommodated by the presence of topotactically ordered arrangements of large localized concentrations of oxide ion vacancies which divide the structure up into microdomains. Experiments have shown that Pr₆O₁₁ can absorb significant amounts of water, even at ambient temperature, apparently by the electrically neutral mechanism proposed by Stotz and Wagner. This involves the absorption of oxide ions at sites where there were previously oxide ion vacancies. Protons are also absorbed, and reside in interstitial sites. Consistent with the high mobility of oxygen in this structure, this water is irreversibly desorbed at relatively low temperatures. Electrochemical experiments will be reported that have been undertaken to investigate the insertion behavior of lithium into these unusual structures, both with and without the initial presence of protons as the result of the absorption of water. Paper presented at the 6th Euroconference on Solid State Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.