Pretreating near infrared spectra with fractional order Savitzky–Golay differentiation(FOSGD)

With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation(FOSGD) is calculated and applied to pretreat near infrared(NIR) spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation(IOSGD),FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.     

New Insights on Volatile Components of Vanilla planifolia Cultivated in Taiwan

Vanilla (Vanilla planifolia) is a precious natural flavoring that is commonly used throughout the world. In the past, all vanilla used in Taiwan was imported; however, recent breakthroughs in cultivation and processing technology have allowed Taiwan to produce its own supply of vanilla. In this study, headspace solid-phase microextraction (HS-SPME) combined with GC-FID and GC-MS was used to analyze the volatile components of vanilla from different origins produced in Taiwan under different cultivation and processing conditions. The results of our study revealed that when comparing different harvest maturities, the composition diversity and total volatile content were both higher when the pods were matured for more than 38 weeks. When comparing different killing conditions, we observed that the highest vanillin percentage was present after vanilla pods were killed three times in 65 °C treatments for 1 min each. From the experiment examining the addition of different strains, the PCA results revealed that the volatiles of vanilla that was processed with Dekkera bruxellensis and Bacillus subtilis was clearly distinguished from which obtained by processing with the other strains. Vanilla processed with B. subtilis contained 2-ethyl-1-hexanol, and this was not detected in other vanillas. Finally, when comparing the vanillin percentage from seven different regions in Taiwan, vanilla percentage from Taitung and Taoyuan Longtan were the highest.     

Inseparable Criterion and Bell Inequality

In this letter, we shall show how to construct constrained Bell-type inequality for a general two-party system, and violating this inequality is equivalent to being inseparable. For 2 × 2 system, the maximum violation is 3, while for 3 × 3 system, the largest violation is 11/3.