In order to obtain the optimal technological conditions of preparing biodiesel, artificial neural network was used to study the biodiesel processing model on transesterification method based on the single factor experiment and orthogonal experiment. The results of experiment indicated that we used the back propagation BP algorithm of artificial neural network to set the network prediction model based on the orthogonal test data can forecast the biodiesel conversion rate under different reaction conditions more accurately.The optimal conditions were obtained from this network model as follows: Molar ratio of methanol to oil was 6:1, the catalyst was 1.0% (w/w, based on oil), reaction temperature and reaction time was 65°Cand 2.5h respectively. Under the optimal conditions, the conversion rate of prediction was 94.93%, the conversion rate of experiment was 95.42% and the relative error was 0.51% compared with the predicted value. Therefore, the network k model could reflect inherent law of sample.

Abstract. In this note , we answer positively a question by Belegradek and Kapovitch[2] about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds admit (complete) metrics with nonnegative curvature.

In order to obtain the optimal technological conditions of preparing biodiesel, artificial neural network was used to study the biodiesel processing model on transesterification method based on the single factor experiment and orthogonal experiment. The results of experiment indicated that we used the back propagation BP algorithm of artificial neural network to set the network prediction model based on the orthogonal test data can forecast the biodiesel conversion rate under different reaction conditions more accurately.The optimal conditions were obtained from this network model as follows: Molar ratio of methanol to oil was 6:1, the catalyst was 1.0% (w/w, based on oil), reaction temperature and reaction time was 65°Cand 2.5h respectively. Under the optimal conditions, the prediction conversion rate was 96.019%, the testing conversion rate was 96.83% and the relative error was 0.84% compared with predicted value. Therefore, the network model could reflect the inherent law of sample.