Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.     

A Photoactivated Cu–CeO2 Catalyst with Cu-[O]-Ce Active Species Designed through MOF Crystal Engineering

Fully utilizing solar energy for catalysis requires the integration of conversion mechanisms and therefore delicate design of catalyst structures and active species. Herein, a MOF crystal engineering method was developed to controllably synthesize a copper–ceria catalyst with well-dispersed photoactive Cu-[O]-Ce species. Using the preferential oxidation of CO as a model reaction, the catalyst showed remarkably efficient and stable photoactivated catalysis, which found practical application in feed gas treatment for fuel cell gas supply. The coexistence of photochemistry and thermochemistry effects contributes to the high efficiency. Our results demonstrate a catalyst design approach with atomic or molecular precision and a combinatorial photoactivation strategy for solar energy conversion.     

An Improved Composite Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods.     

On the output function in a Ginsburg’s machine

We give the form of the output function in Ginsburg’s machine in which the input and output dictionaries are abelian groups and the transition function is of a special form.     

Simultaneous determination of major components of Huangqi–Honghua extract in rat plasma using LC–MS/MS and application to a pharmacokinetic study

A sensitive and reliable LC–MS/MS method was developed and validated for simultaneous quantification of the major components of Huangqi–Honghua extact in rat plasma, including hydroxysafflor yellow A (HSYA), astragaloside IV (ASIV), calycosin‐7‐O‐β‐d ‐glucoside (CAG), calycosin, calycosin‐3′‐O‐glucuronide (C‐3′‐G) and calycosin‐3′‐O‐sulfate (C‐3′‐S). After extraction by protein precipitation with acetonitrile and methanol from plasma, the analytes were separated on a Hypersil BDS C₁₈ column by gradient elution with acetonitrile and 5 mM ammonium acetate. The detection was carried out on a triple quadrupole tandem mass spectrometer equipped with electrospray ionization source switched between negative and positive modes. HSYA was monitored in negative ionization mode from 0 to 4.9 min, and ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S were determined in positive ionization mode from 4.9 to 10 min. The lower limits of quantification of the analytes were 6.25 ng/mL for HSYA, 0.781 ng/mL for CAG and 1.56 ng/mL for ASIV and calycosin. The intra‐ and inter‐assay precision (RSD) values were within 13.43%, and accuracy (RE) ranged from ?8.75 to 9.92%. The validated method was then applied to the pharmacokinetic study of HSYA, ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S in rat after an oral administration of Huangqi–Honghua extract.