The Decomposition and Uniqueness of n-Lie Superalgebras

In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.

Quantitative Analysis of Berberine in Processed Coptis by Near-Infrared Diffuse Reflectance Spectroscopy

The near-infrared（NIR） diffuse reflectance spectroscopy was used to study the content of Berberine in the processed Coptis. The allocated proportions of Coptis to ginger, yellow liquor or Evodia rutaecarpa changed according to the results of orthogonal design as well as the temperature. For as withdrawing the full and effective information from the spectral data as possible, the spectral data was preprocessed through first derivative and multiplicative scatter correetion（MSC） according to the optimization results of different preprocessing methods. Firstly, the model was established by partial least squares（PLS）; the coefficient of determination（R2） of the prediction was 0.839, the root mean squared error of prediction（RMSEP） was 0.1422, and the mean relative error（RME） was 0.0276. Secondly, for reducing the dimension and removing noise, the spectral variables were highly effectively compressed via the wavelet transformation（WT） technology and the Haar wavelet was selected to decompose the spectral signals. After the wavelet coefficients from WT were input into the artificial neural network（ANN） instead of the spectra signal, the quantitative analysis model of Berberine in processed Coptis was established. The R^2 of the model was 0.9153, the RMSEP was 0.0444, and the RME was 0.0091. The values of appraisal index, namely R^2, RMSECV, and RME, indicate that the generalization ability and prediction precision of ANN are superior to those of PLS. The overall results show that NIR spectroscopy combined with ANN can be efficiently utilized for the rapid and accurate analysis of routine chemical compositions in Coptis. Accordingly, the result can provide technical support for the further analysis of Berberine and other components in processed Coptis. Simultaneously, the research can also offer the foundation of quantitative analysis of other NIR application.

On the Gracefulness of Graph(jC_(4n))∪P_m

The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.