C0-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators

Kimura diffusions serve as a stochastic model for the evolution of gene frequencies in population genetics. Their infinitesimal generator is an elliptic differential operator whose second-order coefficients matrix degenerates on the boundary of the domain. In this article, we consider the inhomogeneous initial-value problem defined by generators of Kimura diffusions, and we establish $C^0$-estimates, which allows us to prove that solutions to the inhomogeneous initial-value problem are smooth up to the boundary of the domain where the operator degenerates, even when the initial data is only assumed to be continuous.     

Identification and analysis of chemical constituents and rat serum metabolites in Suan‐Zao‐Ren granule using ultra high performance liquid chromatography quadrupole time‐of‐flight mass spectrometry combined with multiple data processing approaches

Suan‐Zao‐Ren granule is widely used to treat insomnia in China. However, because of the complexity and diversity of the chemical compositions in traditional Chinese medicine formula, the comprehensive analysis of constituents in vitro and in vivo is rather difficult. In our study, an ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry and the PeakView® software, which uses multiple data processing approaches including product ion filter, neutral loss filter, and mass defect filter, method was developed to characterize the ingredients and rat serum metabolites in Suan‐Zao‐Ren granule. A total of 101 constituents were detected in vitro. Under the same analysis conditions, 68 constituents were characterized in rat serum, including 35 prototype components and 33 metabolites. The metabolic pathways of main components were also illustrated. Among them, the metabolic pathways of timosaponin AI were firstly revealed. The bioactive compounds mainly underwent the phase I metabolic pathways including hydroxylation, oxidation, hydrolysis, and phase II metabolic pathways including sulfate conjugation, glucuronide conjugation, cysteine conjugation, acetycysteine conjugation, and glutathione conjugation. In conclusion, our results showed that this analysis approach was extremely useful for the in‐depth pharmacological research of Suan‐Zao‐Ren granule and provided a chemical basis for its rational.     

Hydrophilic interaction liquid chromatography tandem mass spectrometry analysis of malonyl‐coenzyme A in breast cancer cell cultures applying online solid‐phase extraction

Cofactors such as coenzyme A and its derivatives acetyl‐coenzyme A and malonyl‐coenzyme A are involved in many metabolic pathways. Due to trace level concentrations in biological samples and the high reactivity of cofactors, a fast, sensitive, and selective method for quantification is mandatory. In this study, online solid‐phase extraction was coupled successfully to hydrophilic interaction liquid chromatography with tandem mass spectrometry for isolation of analytes in complex matrix and quantification by external calibration. Online solid‐phase extraction was carried out by application of a weak anion‐exchange column, whereas hydrophilic interaction liquid chromatography separation was performed on an amide modified stationary phase. Sample preparation of the extracts before the analysis was reduced to a centrifugation and dilution step. Moreover, the applied online solid‐phase extraction significantly reduced matrix effects and increased the signal‐to‐noise ratio. The limit of detection and the limit of quantification were in the lower nanomolar range. Finally, the applicability of this method was demonstrated on MCF‐7 breast cancer cell cultures, a commonly used model system, where acetyl‐coenzyme A and malonyl‐coenzyme A were determined using standard addition procedure in concentrations of 1.98 μM and 41 nM, respectively.     

Simultaneous determination of pyrametostrobin and its two metabolites in cucumber and soil using a quick,easy, cheap,effective, rugged,and safe method with HPLC–MS/MS

An easy, effective and sensitive analytical method for the simultaneous determination of a novel fungicide pyrametostrobin and its two metabolites pyrametostrobin‐M1 and pyrametostrobin‐M2 in cucumber and soil was developed using a quick, easy, cheap, effective, rugged, and safe method with high‐performance liquid chromatography and tandem mass spectrometry. The extraction solvent was acetonitrile, and cleanup sorbents were primary secondary amine and graphitized carbon black for cucumber samples and primary secondary amine for soil samples. The three target compounds were successfully separated between 3.2 and 3.9 min using a Waters CORTECS™ C₁₈ column connected to an electrospray ionization source. All the matrix‐matched samples at three fortified levels (10, 100 and 1000  μg/kg) provided satisfactory recoveries in the range of 78.8–93.8% with relative standard deviations below 6.9%. The limits of quantitation for the three compounds were below 0.183 μg/kg. The proposed method was validated by analyzing real samples.     

Identification of metabolites in human and rat urine after oral administration of Xiao‐Qing‐Long‐Tang granule using ultra high performance liquid chromatography combined with quadrupole time‐of‐flight mass spectrometry

Xiao‐Qing‐Long‐Tang is a traditional Chinese formula used for the treatment of cold syndrome, bronchitis, and nasal allergies for thousands of years. However, the in vivo integrated metabolism of its multiple components and the active chemical constituents of Xiao‐Qing‐Long‐Tang remain unknown. In this study, a method using ultra high performance liquid chromatography coupled with quadrupole time‐of‐flight tandem mass spectrometry was established for the detection and identification of the metabolites in human and rat urine after oral administration of Xiao‐Qing‐Long‐Tang. A total of 19 compounds were detected or tentatively identified in human urine samples, including eight prototypes and 11 metabolites. Also, a total of 50 compounds were detected or tentatively identified in rat urine samples, including 15 prototypes and 35 metabolites detected with either a highly sensitive extracted ion chromatogram method or the MS^E determination using Mass Fragment software. Our results indicated that phase Ⅱ reactions (e.g. glucuronidation and sulfation) were the main metabolic pathways of flavones, while phase I reactions (e.g. demethylation and hydroxylation) were the major metabolic reaction for alkaloids, lignans, and ginger essential oil. This investigation provided important structural information on the metabolism of Xiao‐Qing‐Long‐Tang and provided evidence to obtain a more comprehensive metabolic profile.     

Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Decimation of the Dyson–Ising ferromagnet

We study the decimation to a sublattice of half the sites of the one-dimensional Dyson–Ising ferromagnet with slowly decaying long-range pair potentials of the form $\frac{1}{{|i?j|}^{\alpha }}$, deep in the phase transition region ($1<\alpha \le 2$ and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ($\alpha >2$) and provides an example of a “standard” non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.     

Continuous spin models on annealed generalized random graphs

We study Gibbs distributions of spins taking values in a general compact Polish space, interacting via a pair potential along the edges of a generalized random graph with a given asymptotic weight distribution $P$, obtained by annealing over the random graph distribution.First we prove a variational formula for the corresponding annealed pressure and provide criteria for absence of phase transitions in the general case.We furthermore study classes of models with second order phase transitions which include rotation-invariant models on spheres and models on intervals, and classify their critical exponents. We find critical exponents which are modified relative to the corresponding mean-field values when $P$ becomes too heavy-tailed, in which case they move continuously with the tail-exponent of $P$. For large classes of models they are the same as for the Ising model treated in Dommers et al. (2016). On the other hand, we provide conditions under which the model is in a different universality class, and construct an explicit example of such a model on the interval.