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The lattice parameters of germanium, rhodium, and iridium were measured with a Unicam 19 cm high-temperature powder camera; the following equations represent the results:

Culture conditions for pullulan production by Aureobasidium pullulans were optimized using response surface methodology at shake flask level without pH control. In the present investigation, a five-level with five-factor central composite rotatable design of experiments was employed to optimize the levels of five factors significantly affecting the pullulan production, biomass production, and sugar utilization in submerged cultivation. The selected factors included concentration of sucrose, ammonium sulphate, yeast extract, dipotassium hydrogen phosphate, and sodium chloride. Using this methodology, the optimal values for concentration of sucrose, ammonium sulphate, yeast extract, dipotassium hydrogen phosphate, and sodium chloride were 5.31%, 0.11%, 0.07%, 0.05%, and 0.15% (w/v), respectively. This optimized medium has projected a theoretically production of pullulan of 4.44%, biomass yield of 1.03%, and sugar utilization of 97.12%. The multiple correlation coefficient 'R' was 0.9976, 0.9761 and 0.9919 for pullulan production, biomass production, and sugar utilization, respectively. The value of R being very close to one justifies an excellent correlation between the predicted and the experimental data.

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