Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

Convergence of multistep methods for Volterra functional differential equations

Summary This paper deals with the convergence of nonstationary quasilinear multistep methods with varying step, used for the numerical integration of Volterra functional differential equations. A Perron type condition (appearing in the differential equations theory) is imposed on the increment function. This gives a generalization of some results of Tavernini ([19–21]).     

Metabolic profile of glyburide in human liver microsomes using LC‐DAD‐Q‐TRAP‐MS/MS

The sulfonylurea urea drug glyburide (glibenclamide) is widely used for the treatment of diabetes milletus and gestational diabetes. In previous studies monohydroxylated metabolites were identified and characterized for glyburide in different species, but the metabolite owing to the loss of cyclohexyl ring was identified only in mouse. Glyburide upon incubation with hepatic microsomes resulted in 10 metabolites for human. The current study identifies new metabolites of glyburide along with the hydroxylated metabolites that were reported earlier. The newly identified drug metabolites are dihydroxylated metabolites, a metabolite owing to the loss of cyclohexyl ring and one owing to hydroxylation with dehydrogenation. Among the 10 identified metabolites, there were six monohydroxylated metabolites, one dihydroxylated metabolite, two metabolites owing to hydroxylation and dehydrogenation, and one metabolite owing to the loss of cyclohexyl ring. New metabolites of glyburide were identified and characterized using liquid chromatography–diode array detector–quadruple‐ion trap–mass spectrometry/mass spectrometry (LC‐DAD‐Q‐TRAP‐MS/MS). An enhanced mass scan–enhanced product ion scan with information‐dependent acquisition mode in a Q‐TRAP‐MS/MS system was used to characterize the metabolites. Liquid chromatography with diode array detection was used as a complimentary technique to confirm and identify the metabolites. Metabolites formed in higher amounts were detected in both diode array detection and mass spectrometry detection. Copyright © 2012 John Wiley & Sons, Ltd.     

In vivo metabolism study of bergenin in rats by HPLC‐QTOF mass spectrometry

Bergenin is the major component of Ardisia creanta sims and Rodgersia sambucifolia hemsl with many biological activities. Although bergenin has been used to treat human diseases in China for man years, there is no report regarding its metabolism. This is the first report to separate and identify the metabolites of bergenin in vivo. In the study, HPLC/Q‐TOF‐MS/MS was used to investigate the metabolites of bergenin in vivo by analyzing the rat body fluid and feces samples. Three metabolites of bergenin were finally identified by the TIC chromatograms, and the structures were also confirmed by their MS² spectra. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthese de Nouveaux Derives Phosphones a Chaine Perfluoree et Leurs Proprietes Adhesives Sur Acier

Ce mémoire décrit la synthèse de phosphonates comportant une chaîne perfluorée. Ces composés sont obtenus par la télomérisation d'allylphosphonates de dialkyle en présence d'un agent de transfert fluoré de type mercaptan. Ensuite, nous employons deux méthodes de déalkylation menant sélectivement soit au monoacide soit au diacide phosphonique. Tous ces produits comprenant une extrémité de chaîne phosphonée, sous forme acide ou ester, ont été caractérisés et leur adhésion respective sur des plaques d'acier est étudiée. Ces tests montrent que le monoacide phosphonique est un excellent promoteur d'adhésion et qu'il est aussi efficace que le diacide. This article describes the synthesis of phosphonic derivatives bearing a perfluorinated chain. These compounds have been synthetized by telomerization of dialkyl allylphosphonate with a fluorinated transfer agent type mercaptan. Then two methods of dealkylation leading selectively were used to mono or to diacid phosphonic moieties. All the products bearing phosphonic end-groups, more or less acidic, have been characterized and their own adhesion on steel plates is studied. These tests show that phosphonic monoacid is an excellent adhesion promoter on steel, as efficient as the diacid compound.     

Characterization of the chemical constituents in Hongjingtian injection by liquid chromatography quadrupole time‐of‐flight mass spectrometry

Hongjingtian injection is made from Rhodiola wallichiana and used in the treatment of stable angina pectoris associated with coronary heart disease. In this study, the chemical constituents in Hongjingtian injection were comprehensively studied using liquid chromatography quadrupole time‐of‐flight mass spectrometry. A total of 49 compounds were identified or assumed, including 10 organic acids, nine phenylethanoids, 10 phenylpropanoids, two flavonoid glycosides, seven monoterpene glycosides, seven octylglycosides and four other types of compounds. The structures of seven compounds were confirmed by comparing their retention times, MS and UV spectra with the corresponding authentic standards. Amongst the 49 compounds, 35 were firstly found in R. wallichiana, while they have been reported in other species of the genus Rhodiola, including Rhodiola crenulata, Rhodiola sacra, Rhodiola rosea and Rhodiola kirilowii. The possible fragmentation pathways in the mass spectrometry of the major types of compounds are proposed and summarized. Our study demonstrates a rapid method for characterizing the chemical constituents present in the Hongjingtian injection, which could also be applied to the identification of chemical constituents in other TCM formulae containing R. wallichiana.     

The profiling and identification of chemical components,prototypes and metabolites of Run‐zao‐zhi‐yang capsule in rat plasma,urine and bile by an UPLC‐Q‐TOF/MSE‐based high‐throughput strategy

Run‐zao‐zhi‐yang (RZZY) capsule, a traditional Chinese medicine formula, is popularly used for the treatment of dermatitis and eczema. However, few studies have been carried out on RZZY and its metabolites. In this study, we developed a three‐step strategy to rapidly characterize the chemical constituents and metabolites of RZZY using ultra‐high‐performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry. A total of 41 chemical components were characterized from RZZY. Among these, there are 11 flavonoids, six alkaloids, six stilbene glycosides, five anthraquinones and 13 other compounds. In addition, 18 prototypes and 35 metabolites were detected in rat plasma, urine and bile. This study offers an applicable approach for high‐throughput profiling and identification of chemical components and metabolites derived from traditional Chinese medicine formula in vivo, and also provides essential data for exploring bioactive ingredients and action mechanisms of RZZY.     

Double Aztec diamonds and the tacnode process

Discrete and continuous non-intersecting random processes have given rise to critical “infinite-dimensional diffusions”, like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary.