We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
Decomposition promoting factors and extraction process of tungsten carbide and tungstic acid powders in the zinc decomposition process of tungsten scraps which are composed mostly of tungsten carbide and cobalt were evaluated. Zinc volatility was suppressed by the enclosed graphite crucible and zinc volatilization pressure was produced in the reaction graphite crucible inside an electric furnace for ZDP (Zinc Decomposition Process). Decomposition reaction was done for 2hours at 650°, which 100% decomposed the tungsten scraps that were over 30 mm thick. Decomposed scraps were pulverized under 75μm and were composed of tungsten carbide and cobalt identified by the XRD (X-ray Diffraction). To produce the WC(Tungsten Carbide) powder directly from decomposed scraps, pulverized powders were reacted with hydrochloric acid to remove the cobalt binder. Also to produce the tungstic acid, pulverized powders were reacted with aqua regia to remove the cobalt binder and oxidize the tungsten carbide. Tungsten carbide and tungstic acid powders were identified by XRD and chemical composition analysis.
Typical oxidation process of tungsten scraps was modified by the rotary kiln with oxygen burner to increase the oxidation rate of tungsten scraps. Also to accelerate the solubility of solid oxidized products, the hydrothermal reflux method was adapted. By heating tungsten scraps in rotary kiln with oxygen burner at around 900° for 2hrs, the scraps was oxidized completely. Then oxidized products (WO3 and CoWO4) was fully dissolved in the solution of NaOH by hydrothermal reflux method at 150° for 2hrs. The dissolution rate of oxidized products was increased with increasing the reaction temperature and concentration of NaOH. And then CaWO4 and H2WO4 could be generated from the aqueous sodium tungstate solution. Ammonium paratungstate (APT) also could be produced from tungstic acid using by aqueous ammonium solution. The morphologies (cubic and plate types) of APT was controlled by the stirring process of purified solution of ammonium paratungstate.
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