Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

Numerical Investigation On Detonation Cell Evolution In A Channel With Area-Changing Cross Section

The two-dimensional cellular detonation propagating in a channel with area-changing cross section was numerically simulated with the dispersion-controlled dissipative scheme and a detailed chemical reaction model. Effects of the flow expansion and compression on the cellular detonation cell were investigated to illustrate the mechanism of the transverse wave development and the cellular detonation cell evolution. By examining gas composition variations behind the leading shock, the chemical reaction rate, the reaction zone length, and thermodynamic parameters, two kinds of the abnormal detonation waves were identified. To explore their development mechanism, chemical reactions, reflected shocks and rarefaction waves were discussed, which interact with each other and affect the cellular detonation in different ways.

The Relationship between Decision Trees and the Scale of Train Data Set

Decision Trees need train samples in the train data set to get classification rules. If the number of train data was too small, the important information might be missed and thus the model could not explain the classification rules of data. While it is not affirmative that large scale of train data set can get well model. This Paper analysis the relationship between decision trees and the train data scale. We use nine decision tree algorithms to experiment the accuracy, complexity and robustness of decision tree algorithms. Some results are demonstrated.