Simultaneous quantification of five major constituents in stems of Dracaena plants and related medicinal preparations from China and Vietnam by HPLC–DAD

A high‐performance liquid chromatographic (HPLC) method was developed for the simultaneous quantification of five major bioactive constituents in the stems of resiniferous Dracaena plants from China and Vietnam, as well as those in the related traditional Chinese medicinal preparations. A diode array detector with the wavelength of 330 nm was used to monitor resveratrol, 7,4′‐dihydroxyflavone and pterostilbene, while loureirin A and loureirin B were monitored at 280 nm. The five constituents were separated on an Agela SB C₁₈ column by gradient elution using 0.008% (v/v) formic acid solution (A) and acetonitrile (B) as the mobile phase. The validation of the method included recovery, linearity, accuracy and precision (intra‐ and inter‐day variation). The range of recoveries of this method was 98.1–104.9%, with all the constituents showing good linearity (r² > 0.9999). The accuracy and precision were satisfactory, with the overall intra‐ and inter‐day variation being less than 4%. The present method has been successfully applied for the determination of all five constituents in 21 related herbal samples including 10 D. cochinchinensis stem samples, seven D. cambodiana stem samples and four purchased medicinal preparations. The contents of these constituents were analyzed using principal component analysis, which can efficiently identify raw herb of Dracaena from different sources. The study may be considered helpful to the quality control of Dracena plants and its medicinal preparations. Copyright © 2009 John Wiley & Sons, Ltd.     

The multivariate N-Component resolution problem with minimum assumptions

The present state of the minimum assumption multivariate component resolution theory is outlined. Some new developments are presented: limiting function domains; the analytical expression for the limiting function; efficient algorithms for defining the FIRPOL and INNPOL hyperpolyhedrons. A very low resolution data set is analyzed.     

Integral formula of Minkowski type and new characterization of the Wulff shape

Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.     

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.     

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization of Chickpea Flour by Near Infrared Spectroscopy and Chemometrics

Near infrared (NIR) spectrometry was used for the rapid characterization of quality parameters in desi chickpea flour (besan). Partial least square regression, principal component regression (PCR), interval partial least squares (iPLS), and synergy interval partial least squares (siPLS) were used to determine the protein, carbohydrate, fat, and moisture concentrations of besan. Spectra were collected in reflectance mode using a lab-built predispersive filter-based instrument from 700 to 2500?nm. The quality parameters were also determined by standard methods. The root mean square error (RMSE) for the calibration and validation sets was used to evaluate the performance of the models. The correlation coefficients for moisture, fat, protein, and carbohydrates in chickpea flour exceeded 0.96 using PLS and PCR models using the full spectral range. Wavelengths from 2100 to 2345?nm had the lowest RMSE for quality parameters by iPLS. The error was further decreased by 0.41, 0.1, and 1.1% for carbohydrates, fats, and proteins by siPLS. The NIR spectral regions yielding the lowest RMSE of prediction were 1620–2345?nm for carbohydrates, 1180–1590?nm and 1860–2094?nm for fat, and 1700–2345?nm for proteins. The study shows that chickpea flour quality parameters were accurately determined using the optimized wavelengths.     

含三次耦合项的两自由度Duffing系统的共振及混沌行为

研究了一类含三次耦合项的两自由度Duffing系统的动力学行为。首先应用多尺度方法近似求解系统的一阶稳态响应。通过讨论系统的主共振和1∶1内共振,分析了三次耦合项对系统响应的影响。随后研究系统随外加周期力强度变化的分岔过程,发现除了常见的倍周期分岔通向混沌外,还存在一种直接由周期运动进入混沌的突发路径。结合对系统的最大Lyapunov指数,相轨图及Poincar啨映射的分析验证了上述结论。     

主应力迹线的自动绘制

主应力迹线是代表主应力方向的曲线簇。在土木建筑工程中主应力迹线是布筋方向的依据,但是在工程中通常都是徒手或用曲线板近似绘制主应力迹线。作者提出一种新的主应力迹线自动的绘制方法。该方法是根据主应力迹线满足过任意三条等倾线的主应力都可以用二次曲线来描述这一条件,再利用主应力迹线本身所具有的性质列出方程组解算出描述主应力迹线的一元二次方程,然后根据方程描绘出所求的主应力迹线。实验证明这种方法对于工程上进行主应力迹线的绘制很有效。     

A failure of a class of K-BKZ equations based on principal stretches

The invariants in the K-BKZ constitutive equation for an incompressible viscoelastic fluid are usually taken to be the trace of the Finger strain tensor and its inverse. The basis for this choice of invariants is not derived from the K-BKZ theory, but rather is due to the perception that this is the most natural choice. Research into using other sets of invariants in the K-BKZ equation, such as the principal stretches or the eigenvalues of the Finger strain tensor (i.e., the squares of the principal stretches) is relatively new. We attempt here to derive a K-BKZ equation based on the squares of the principal stretches that models the behavior of a low-density polyethylene melt in simple shear and uniaxial elongational deformation. In doing so, two assumptions are made as to the form of the strain-dependent energy function: first, that there is a function f(q) such that the energy function can be written as the sum of f(q _i ),i = 1, 2, 3, where the q _i 'sare the squares of the principal stretches, and second that f is a power law. We find that the K-BKZ equation resulting from these two assumptions is inadequate to describe both the shear and elongational behavior of our material and we conclude that the second of the above assumptions is not valid. Further investigation, including predictions of the second normal stress difference and some finite element calculations reveals that the first assumption is also invalid for our material.