N-distance tests for a composite hypothesis of goodness of fit

In this paper, we consider an application of N-distance theory for testing composite hypotheses of goodness of fit. This work is a continuation of our research started in [A. Bakshaev, Goodness of fit and homogeneity tests on the basis of N-distances, J. Stat. Plan. Inference, 139(11):3750–3758, 2009; A. Bakshaev, Nonparametric tests based on N-distances, Lith. Math. J., 48(4):368–379, 2008]. Particular attention is paid to normality and exponentiality tests. A comparative Monte Carlo power study for the proposed criteria is provided. Different alternatives in uni- and bivariate cases are investigated.     

Application of high‐field NMR spectroscopy for characterization and quantitation of submilligram quantities of isolated natural products

We have investigated and compared a number of sample conditions on different NMR platforms in the search of maximum SNR and optimal experiment time efficiency for structure elucidation and quantitation of natural products. Using restricted volume 3 mm Shigemi microcell assembly in conjunction with a 900 MHz NMR spectrometer equipped with a 5 mm carbon‐sensitive inverse cryoprobe, it was possible to achieve a substantial increase in SNR (46‐fold) as compared with a conventional room temperature 400 MHz instrument. Switching from standard 5 mm NMR tube to 3 mm Shigemi microcell assembly typically improved SNR by threefold on either 600 or 900 MHz cryoplatform. A quantitation method that relies on a calibrated residual protonated NMR solvent signal as internal standard was developed using the same hardware setup and restricted sample volume tubes. Linearity of the method spans over 3 orders of magnitude, from low microgram to milligram quantities. We successfully applied this method to quantify a low micrgram sample of paclitaxel, verified by a UV/VIS quantitation measurement. Copyright © 2015 John Wiley & Sons, Ltd.