Synthesis of 2‐Arylbenzoxazoles from Flash Vacuum Pyrolysis of 2‐Methoxy‐N‐(arenylidene)anilines

Flash vacuum pyrolysis of 2‐methoxy‐N‐(arenylidene)anilines 2a‐g at 700 °C and 1 × 10^‐2 Torr gave the corresponding 2‐arylbenzoxazoles 1a‐g .     

Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism

The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.     

The linear combinations of biomarkers which maximize the partial area under the ROC curves

As biotechnology has made remarkable progress nowadays, there has also been a great improvement on data collection with lower cost and higher quality outcomes. More often than not investigators can obtain the measurements of many disease-related features simultaneously. When multiple potential biomarkers are available for constructing a diagnostic tool of a disease, an effective approach is to combine these biomarkers to build one single indicator. For continuous-scaled variables, the use of linear combinations is popular due to its easy interpretation. Su and Liu (J Ame Stat Assoc 88(424):1350–1355, 1993) derived the best linear combination under the criterion of the area under the receiver operating characteristic (ROC) curve, when the joint normality of biomarkers is assumed. However, in many investigations, the emphases are placed only on a limited extent of clinical relevancy, instead of the whole ROC curve. The goal of this study is to find the linear combination that maximizes the partial area under a ROC curve (pAUC) for a pre-specified range. In order to find an analytic solution, the first derivative of the pAUC under normal assumption is derived. The explicit form is so complicated, that a further validation on the Hessian matrix is difficult. On the other hand, we find that the pAUC maximizer may not be unique and local maximizers do exist in some cases. Consequently, the existing algorithms find an initial-point dependent solution and are inadequate to serve our needs. Hence, we propose a new algorithm by adopting several initial points at one time. Intensive numerical studies have been performed to show the adequacy of the proposed algorithm. Real examples are also provided for illustration.     

Perfect transmission of spin waves in a one-dimensional magnonic quasicrystal

Existence of the perfect transmission resonances of spin waves in a one-dimensional Thue–Morse magnonic quasicrystal is proposed. We find that occurrence of the perfect transmission just corresponds to the repeated bandedges in the bandedge map. Frequencies at the perfect transmissions for system with arbitrary generation order can be predicted by the bandedge map of the second and third order systems using two iterative schemes. These results show that density of the perfect transmission resonance increases exponentially for increasing the order of the system. However, the perfect transmissions are kept for higher order systems even if the peaks become denser.     

Trace Determination of Benzalkonium Chlorides in River and Wastewater by Capillary Electrophoresis following Solid‐Phase Extraction Coupled with Salting‐Out Extraction

Trace levels analysisbenzalkonium chlorides (BAKs) in river water and wastewater treatment plants (WWTP) effluents were determined by capillary electrophoresis (CE) following solid‐phase extraction (SPE) and salting‐out extraction. Salting‐out extraction using an appropriate ratio of sodium chloride (NaCl) and acetonitrile (ACN) mixed with concentrated SPE elutant was capable of providing more than 500‐fold enhancement in detection sensitivity. The ratios of ACN and NaCl for salting‐out extraction were investigated and optimized. Matrix interference was eliminated by salting‐out extraction. Limits of quantitation of BAK homologues were achieved at 0.1 μg/L in 250 mL water samples. Recoveries of BAKs in various spiked water samples ranged from 70% to 84% with relative standard deviation (RSD) less than 9%. Trace amounts of total BAKs were detected in river water and WWTP effluent samples ranging from 27 to 145 μg/L at the first time by CE.