On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.     

常系数非齐次线性微分方程的特解公式

给出了一类常系数非齐次线性微分方程的特解的计算公式.     

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与经典Cramer-Lundberg风险模型中保费收取过程 是时间的线性函数不同, 我们考虑聚合的保费收取过程是复合Poisson过程, 研究了在此模型下的常数分红策略问题. Dickson和Waters,(2004)指出在破产发生时, 股东还应有责任偿付破产时的赤字. 因此, 在本文中考虑的最优准则是最大化破产发生前的分红折现值与破产发生时赤字的差的期望. 做为例子, 当个体保费收取额和索赔额均为指数分布时, 给出了计算分红障碍的条件     

A novel two-nozzle electrospinning process for preparing microfiber reinforced pH-sensitive nano-membrane with enhanced mechanical property

A novel pH sensitive membrane (pHS-M) with mechanical integrity is synthesized firstly by two nozzles electrospining in this work. We report an excellent strategy here to combine indicative nanofiber from 9% PAN solution and micro-sized fibers from 20% PA-66 solution homogeneously in one electrospinning setup. The pH indicative property of electrospun sheet can be achieved by PAN nanofibers that first aminating with ethylenediamine and then immobilizing phenolphthalein covalently through a Mannich reaction, while micro-sized PA-66 fibers are responsible for the improvement of mechanical property of electrospun mat due to their elastic and flexible behavior. The composite membrane was characterized by SEM, FTIR and UV–vis spectroscopy. Results show that two kinds of pH sensitive membranes (single PAN nanofibers (pHS-NF) or composite PAN/PA-66 fiber (pHS-CF)) all exhibited remarkable color change from pale yellow to violet in a wide range of alkaline solution and rapid response time within 100 s. But after added of microfiber, the tensile strength was enhanced from 1.3 MPa to 6.90 MPa prominently which is beneficial to put the membrane into practice.     

In vivo solid-phase microextraction for single rodent pharmacokinetics studies of carbamazepine and carbamazepine-10,11-epoxide in mice

The use of solid-phase microextraction (SPME) for in vivo sampling of drugs and metabolites in the bloodstream of freely moving animals eliminates the need for blood withdrawal in order to generate pharmacokinetics (PK) profiles in support of pharmaceutical drug discovery studies. In this study, SPME was applied for in vivo sampling in mice for the first time and enables the use of a single animal to construct the entire PK profile. In vivo SPME sampling procedure used commercial prototype single-use in vivo SPME probes with a biocompatible extractive coating and a polyurethane sampling interface designed to facilitate repeated sampling from the same animal. Pre-equilibrium in vivo SPME sampling, kinetic on-fibre standardization calibration and liquid chromatography–tandem mass spectrometry analysis (LC–MS/MS) were used to determine unbound and total circulating concentrations of carbamazepine (CBZ) and its active metabolite carbamazepine-10,11-epoxide (CBZEP) in mice (n = 7) after 2 mg/kg intravenous dosing. The method was linear in the range of 1–2000 ng/mL CBZ in whole blood with acceptable accuracy (93–97%) and precision (<17% RSD). The single dose PK results obtained using in vivo SPME sampling compare well to results obtained by serial automated blood sampling as well as by the more conventional method of terminal blood collection from multiple animals/time point. In vivo SPME offers the advantages of serial and repeated sampling from the same animal, speed, improved sample clean-up, decreased animal use and the ability to obtain both free and total drug concentrations from the same experiment.     

In-vial pyrolysis (PyroVial) with pre- and post-sample treatment combined with different chromatographic techniques

A new generic pyrolysis unit (PyroVial) is presented. Pyrolysis is carried out in a 2 mL autosampler vial placed in a XYZ robot for automated pyrolysis as well as for pre- and post-pyrolysis treatment of the sample. Analysis of the volatiles is performed by headspace analysis while the semi- and non-volatiles are extracted from the pyrolysate with an organic solvent. The features of the PyroVial are such that all chromatographic techniques can be applied. The pyrolysis unit is discussed in terms of its technical features and its performance is illustrated with applications including conventional pyrolysis, in situ and post-pyrolysis derivatization, reaction pyrolysis and catalytic cracking.     

Fabrication of graphene/poly(methyl methacrylate) composite electrode for capillary electrophoretic determination of bioactive constituents in Herba Geranii

This report describes the development and application of a novel graphene/poly(methyl methacrylate) composite electrode as a sensitive amperometric detector of capillary electrophoresis. The composite electrode was fabricated on the basis of the in situ polymerization of a mixture of graphene and prepolymerized methyl methacrylate in the microchannel of a piece of fused silica capillary under heat. SEM, XRD and FT-IR offered insights into the nature of the composite. The results indicated that graphenes were well dispersed in the composite to form an interconnected conducting network. The performance of this unique graphene-based detector has been demonstrated by separating and detecting seven naturally occurring phenolic compounds in Herba Geranii in combination with capillary electrophoresis. The graphene-based detector offered significantly lower operating potentials, substantially enhanced signal-to-noise characteristics, and lower expense of operation. The simplicity and significant performance exhibited by the graphene/poly(methyl methacrylate) composite electrode also indicate great promise for microchip CE, flowing injection analysis, and other microfluidic analysis systems.     

Direct dynamics study on mechanism and kinetics of the biradical self‐reaction of HOO

A theoretical study of the mechanism and the kinetics for the hydrogen abstraction reaction of the biradical hydroperoxy radical has been presented at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) level of theory. Our theoretical calculations suppose a stepwise mechanism involving the formation of a postreactant complex in the triplet and singlet entrance channels. Four transition states of the six‐membered chain complexes (³TS1 and ¹TS1) and six‐membered ring complexes (³TS2 and ¹TS2) are located at the high dual level CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) method. The rate constants of Path 1 ～ Path 4 at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G (d,p) level are calculated by means of the conventional transition state theory (TST) and canonical variational TST without and with small‐curvature tunneling (SCT) correction within the temperature range of 200–2,500 K. The calculated results show that the triplet channel is the dominating reaction channel and Path 2 is found to be the most favorable pathway. The rate constants of Path 2 are in good agreement with the experimental values at the experimentally measured temperatures. Moreover, the variational effect is not obvious in the low temperature range but is not neglectable in the high temperature range. The SCT plays an important role particularly in the low temperature range. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Deletion and contraction identities for the resistance values and the Kirchhoff index

We establish identities, which we call deletion and contraction identities, for the resistance values on an electrical network. As an application of these identities, we give an upper bound to the Kirchhoff index of a molecular graph. Our upper bound, expressed in terms of the set of vertices and the edge connectivity of the graph, improves previously known upper bounds. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010