Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Automorphisms of flag systems

We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge–Ampère type equations (2nd order). Next, we describe a prolongation functor operating on the infinitesimal symmetries (automorphisms) of the Darboux flag and extending these, isomorphically, to all the symmetries of any other flag. Hence, flag systems cannot be distinguished by their symmetry algebras and the local classification of these objects is approached by considering higher order isotropies of these algebras as well as the groupoids of k-th order formal equivalences since the differential equations defining the latter provide precious information for the application of flag systems to differential equations (e.g., Cartan's criterion for non-linear Monge equations). In examining the behavior of the isotropy algebras, that can either diminish or remain the same, when passing from a derived system $S_{\nu }$ to the consecutive system $S_{\nu +1}$, we obtain a full set of numerical invariants for the elementary flag systems that moreover specifies the local models.     

Liquid chromatography‐tandem mass spectrometry assay for the simultaneous determination of three major flavonoids and their glucuronidated metabolites in rats after oral administration of Artemisia annua L. extract at a therapeutic ultra‐low dose

The traditional antimalarial herb Artemisia annua L., from which artemisinin is isolated, is widely used in endemic regions. It has been suggested that artemisinin activity can be enhanced by flavonoids in A. annua; however, how fast and how long the flavonoids are present in the body remains unknown. In the present study, a rapid and sensitive liquid chromatography with tandem mass spectrometry method was developed and validated for the simultaneous determination of three major flavonoids components, i.e. chrysosplenol D, chrysoplenetin, and artemetin and their glucuronidated metabolites in rats after oral administrations of A. annua extracts at a therapeutic ultra‐low dose. The concentration of the intact form was determined directly, and the concentration of the glucuronidated form was assayed in the form of flavonoids aglycones, after treatment with β‐glucuronidase/sulfatase. The method was linear in the range of 0.5–300.0 ng/mL for chrysoplenetin and artemetin, and 2–600 ng/mL for chrysosplenol D. All the validation data conformed to the acceptance requirements. The study revealed a significantly higher exposure of the flavonoid constituents in conjugated forms in rats, with only trace intact from. Multiple oral doses of A. annua extracts led to a decreased plasma concentration levels for three flavonoids.     

Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Identification of metabolites of rupestonic acid in rat urine by liquid chromatography combined with electrospray ionization quadrupole time‐of‐flight tandem mass spectrometry

Rupestonic acid, a potential anti‐influenza agent, is an important and characteristic compound in Artemisia rupestris L., a well‐known traditional Uighur medicine for the treatment of colds. In the present study, high‐performance liquid chromatography combined with electrospray ionization quadrupole time‐of‐flight tandem mass spectrometry was used to detect and identify the metabolites in rat urine after oral administration of rupestonic acid. A total of 10 metabolites were identified or partially characterized. The structure elucidations of the metabolites were performed by comparing the changes in accurate molecular masses and fragment ions with those of the parent compound. The results showed that the main metabolites of rupestonic acid in rat urine were formed by oxidation, hydrogenation and glucuronidation. A metabolism pathway was proposed for the first time based on the characterized structures. This metabolism study can provide essential information for drug discovery, design and clinical application of rupestonic acid. Copyright © 2014 John Wiley & Sons, Ltd.     

Studies on metabolites and metabolic pathways of bulleyaconitine A in rat liver microsomes using LC‐MSn combined with specific inhibitors

Bulleyaconitine A (BLA) from Aconitum bulleyanum plants is usually used as anti‐inflammatory drug in some Asian countries. It has a variety of bioactivities, and at the same time some toxicities. Since the bioactivities and toxicities of BLA are closely related to its metabolism, the metabolites and the metabolic pathways of BLA in rat liver microsomes were investigated by HPLC–MSⁿ. In this research, the 12 metabolites of BLA were identified according to the results of HPLC‐MSⁿ data and the relevant literature. The results showed that there are multiple metabolites of BLA in rat liver microsomes, including demethylation, deacetylation, dehydrogenation deacetylation and hydroxylation. The major metabolic pathways of BLA in rat liver microsomes were clarified by HPLC‐MS combined with specific inhibitors of CYP450 isoforms. As a result, CYP3A and 2C were found to be the principal CYP isoforms contributing to the metabolism of BLA. Moreover, CYP2D6 and 2E1 are also more important CYP isoforms for the metabolism of BLA. While CYP1A2 only affected the formation rate of M11, its effect on the metabolism of BLA is very small. Copyright © 2014 John Wiley & Sons, Ltd.     

Metabolic profiles of dioscin in rats revealed by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry

Dioscin (DIS), one of the most abundant bioactive steroidal saponins in Dioscorea sp., is used as a complementary medicine to treat coronary disease and angina pectoris in China. Although the pharmacological activities and pharmacokinetics of DIS have been well demonstrated, information regarding the final metabolic fates is very limited. This study investigated the in vivo metabolic profiles of DIS after oral administration by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry method. The structures of the metabolites were identified and tentatively characterized by means of comparing the molecular mass, retention time and fragmentation pattern of the analytes with those of the parent compound. A total of eight metabolites, including seven phase I and one phase II metabolites, were detected and tentatively identified for the first time. Oxidation, deglycosylation and glucuronidation were found to be the major metabolic processes of the compound in rats. In addition, a possible metabolic pathway on the biotransformation of DIS in vivo was proposed. This study provides valuable and new information on the metabolism of DIS, which will be helpful for further understanding its mechanism of action. Copyright © 2015 John Wiley & Sons, Ltd.     

Plasma metabolomics analysis of endogenous and exogenous metabolites in the rat after administration of Lonicerae Japonicae Flos

Lonicerae Japonicae Flos (LJF) is a typical herbal medicine and is used as a functional food. LJF, which has complex chemical compounds, has various biological effects. The global metabolomics, focusing on both the endogenous and exogenous metabolites, have not yet been investigated for LJF in normal healthy rats using LC–MS. In this study, plasma metabolomics was analyzed after the administration of LJF at different time intervals, and the exogenous metabolites were identified. Partial least squares discriminant analysis showed significant differences in chemical content in the dosed rats. Cholic acid, indoleacrylic acid, indolelactic acid, hippuric acid, N-acetyl-phenylalanine, and N-acetyl-serotonin significantly accumulated in the dosed rats. Lysophosphatidylethanolamine and lysophosphatidylcholine content, including plasmalogen, increased. There were 25 components of LJF, including 15 prototypes and 10 metabolites, that were identified. The 15 prototypes included phenolic acids, flavonoids, and iridoids, and their contents decreased with an increase in the administration time. Glucuronidation and sulfation of polyphenols were found for LJF. The exogenous glucuronide and sulfate metabolites—including dihydrocoumaric acid-sulfate, dihydrocaffeic acid-sulfate, dihydroferulic acid-sulfate, apigenin-glucuronide, apigenin-glucuronide-sulfate, isorhamnetin-glucuronide-sulfate, and others—were identified with a neutral loss of 176 and 80, respectively. The metabolic differences found in the study may serve as biomarkers of LJF consumption and promote the understanding of the mechanism of action of LJF.