The Riesz basis property of discrete operators and application to a Euler-Bernoulli beam equation with boundary linear feedback control

In this paper, we give an abstract condition of Riesz basisgeneration for discrete operators in Hilbert spaces, from whichwe show that the generalized eigenfunctions of a Euler–Bernoullibeam equation with boundary linear feedback control form a Rieszbasis for the state Hilbert space. As an consequence, the asymptoticexpression of eigenvalues together with exponential stabilityare readily presented.     

New approach on similarity analysis of chromatographic fingerprint of herbal medicine

A new approach to the construction and similarity analysis of chromatographic fingerprint for herbal medicine is presented in this paper. Samples of chuanxiong, a herbal medicine for headache, from three producing areas of China were used to evaluate the utility of this study. The samples were analyzed with high-performance liquid chromatography (HPLC) and the peak areas of the chromatograms were used to construct the fingerprints of the herbal medicines. A vector of differences was defined between the two fingerprints. The scalar mean of the difference vector was taken as a statistic and both the t-test and Bayesian hypothesis testing were implemented to provide a one-to-one comparison of the fingerprints. Compared with principal component analysis (PCA), correlation coefficient and vector cosine, the new method offers a better differentiation of the similarity or difference between the fingerprints from same sample of chuanxiong. When the new method was used in the similarity analysis of the fingerprints of chuanxiong from different production areas, a clear-cut signature was obtained that reveals the significant difference between them.