On the Meromorphic Solutions of Fermat-Type Differential Equations

In this paper, we investigate the meromorphic solutions of the Fermat-type differential equations f’(z)n + f(z+c)m = eAz+B (c ≠ 0) over the complex plane C for positive integers m, n, and A, B, c are constants. Our results improve and extend some earlier results given by Liu et al. Moreover, some examples are presented to show the preciseness of our results.

Optimization of rice wine fermentation process based on the simultaneous saccharification and fermentation kinetic model

Chinese rice wine making is a typical simultaneous saccharification and fermentation （SSF） process. During the fermentation process, temperature is one of the key parameters which decide the quality of Chinese rice wine. To optimize the SSF process for Chinese rice wine brewing, the effects of temperature on the kinetic parameters of yeast growth and ethanol production at various temperatures were determined in batch cultures using a mathematical model. The kinetic parameters as a function of temperature were evaluated using the software Origin8.0. Combing these functions with the mathematical model, an appropriate form of the model equations for the SSF considering the effects of temperature were developed. The kinetic parameters were found to fit the experimental data satisfactorily with the developed temperature-dependent model. The temperature profile for maximizing the ethanol production for rice wine fermentation was determined by genetic algorithm. The optimum temperature profile began at a low temperature of 26℃ up to 30 h. The operating temperature increased rapidly to 31.9 ℃, and then decreased slowly to 18℃ at 65 h. Thereafter, the temperature was maintained at 18 ℃ until the end of fermentation. A maximum ethanol production of 89.3 g.L 1 was attained. Conceivably, our model would facilitate the improvement of Chinese rice wine production at the industrial scale.