Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Development and validation of a reversed‐phase HPLC method for CYP1A2 phenotyping by use of a caffeine metabolite ratio in saliva

CYP1A2 is important for metabolizing various clinically used drugs. Phenotyping of CYP1A2 may prove helpful for drug individualization therapy. Several HPLC methods have been developed for quantification of caffeine metabolites in plasma and urine. Aim of the present study was to develop a valid and simple HPLC method for evaluating CYP1A2 activity during exposure in xenobiotics by the use of human saliva. Caffeine and paraxanthine were isolated from saliva by liquid‐liquid extraction (chlorophorm/isopropanol 85/15v/v). Extracts were analyzed by reversed‐phase HPLC on a C₁₈ column with mobile phase 0.1% acetic acid/methanol/acetonitrile (80/20/2 v/v) and detected at 273nm. Caffeine and paraxanthine elution times were <13min with no interferences from impurities or caffeine metabolites. Detector response was linear (0.10–8.00µg/ml, R²>0.99), recovery was >93% and bias <4.47%. Intra‐ and inter‐day precision was <5.14% (n=6). The limit of quantitation was 0.10µg/ml and the limit of detection was 0.018±0.002µg/mL for paraxanthine and 0.032±0.002µg/ml for caffeine. Paraxanthine/caffeine ratio of 34 healthy volunteers was significantly higher in smokers (p<0.001). Saliva paraxanthine/caffeine ratios and urine metabolite ratios were highly correlated (r=0.85, p<0.001). The method can be used for the monitoring of CYP1A2 activity in clinical practice and in studies relevant to exposure to environmental and pharmacological xenobiotics. Copyright © 2015 John Wiley & Sons, Ltd.