Multiplication maps and vanishing theorems for Toric varieties

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.     

Preparation of LiNiO2 and LiM y Ni1- y O2 (M=Co,Al) films by electrostatic spray deposition

Syntheses of LiNiO₂, LiCo_0.5Ni_0.5O₂, and LiAl_0.25Ni_0.75O₂ as thin films were carried out by electrostatic spray deposition (ESD) onto a gold substrate. Single-phase LiNiO₂ film was obtained using a precursor solution of Li(OCOCH₃)+Ni(OCOCH₃)₂/ethanol, and by heating the deposit at 700 °C under an oxygen stream. In the case of cobalt or aluminum doping, Co(NO₃)₂/ethanol or Al(NO₃)₃/ethanol were added to the precursor solution in a given ratio. X-ray diffractometry revealed that all films had a crystal structure of space group R3ˉm; a=2.879, c=14.197 ? for LiNiO₂; a=2.844, c=14.152 ? for LiCo_0.5Ni_0.5O₂; a=2.855, c=14.148 ? for LiAl_0.25Ni_0.75O₂ (in hexagonal setting). Although these products were highly porous, it was observed that the average film thickness of LiNiO₂ increased almost proportionally with the deposition time. Electrochemical measurements (cyclic voltammetry, charge/discharge measurement at a constant current) were carried out in organic solutions of LiClO₄ (1 mol dm⁻³ LiClO₄/propylene carbonate+ethylene carbonate). The results indicated that thin films fabricated by ESD were electrochemically active for lithium ion extraction/insertion. The effect of cobalt or aluminum doping on the voltammograms is also described. Received: 1 April 1998 / Accepted: 23 July 1998     

Determination of sulfur in metal sulfides by bromine water-CCl4 oxidative dissolution and modified EDTA titration

The sulfur content in metal sulfides can be determined after oxidative dissolution with bromine water-CCl₄ at 50 °C by modified EDTA titration. The sulfides were quantitatively oxidized to SO₄ ^2– without evolving H₂S, and the metal cations were removed by cation exchange on an H-type column. Sulfate was precipitated as BaSO₄, and the remaining Ba²⁺ was subsequently titrated with EDTA at pH = 10. The standard deviation for the determined sulfur in the metal sulfides, some of which can be hardly dissolved in usual mineral acid media, is about a few %. The method can be carried out with sample amounts containing as little as 1.5–2 mg sulfur. Received: 31 July 1997 / Revised: 5 January 1998 / Accepted: 9 January 1998     

Ion conductivity of poly(ethylene oxide)-based polyurethane networks containing alkali metal salts

Ion conductivity of poly(ethylene oxide) (PEO)-based polyurethane networks containing alkali metal salts has been investigated. Consequently, it has been revealed that the conductivity is dependent on the following parameters: lattice energy of the alkali metal salt, concentration of alkali metal salt, and the cross-linking density of the network polymer (which is a function both of the amount of cross-linking agent and the molecular weight of PEO). Under optimal conditions, the conductivity at ambient temperature corresponded to 2.51 × 10^?5 Scm^?1, which is greater than that of a typical alkali metal-PEO system by a factor of about 10² to 10³. Moreover, from the standpoint of the application to electrochromic displays (ECD), tensile bond strength between the polymer electrolytes and tungsten trioxide (WO₃), which is the most promising electrochromic material, has been evaluated. The bonding strength of the bond of WO₃ with the present electrolyte has been found to be much larger than that of the alkali metal-PEO system.