Achieving Brouwer’s law with implicit Runge–Kutta methods

In high accuracy long-time integration of differential equations, round-off errors may dominate truncation errors. This article studies the influence of round-off on the conservation of first integrals such as the total energy in Hamiltonian systems. For implicit Runge–Kutta methods, a standard implementation shows an unexpected propagation. We propose a modification that reduces the effect of round-off and shows a qualitative and quantitative improvement for an accurate integration over long times. AMS subject classification (2000)  65L06, 65G50, 65P10     

Study on a hidden protein-DNA binding in salmon sperm DNA sample by dynamic kinetic capillary isoelectric focusing

Nuclease P1 is an important enzyme that hydrolyzes RNA or single-stranded DNA into nucleotides, and complete digestion is an essential basis for assays based on this enzyme. To digest a doubled-stranded DNA, the enzyme is usually combined with heat denaturing, which breaks doubled-stranded DNA into single strands. This paper presents an un-expected phenomenon that nuclease P1, in combination with heat denaturing, fails to completely digest a DNA sample extracted from salmon sperm. Under the experimental conditions used, at which nuclease P1 can completely digest calf thymus DNA, the digestion yield of salmon sperm DNA was only 89.5%. Spectrometric measurement indicated that a total protein of 4.7% is present in the DNA sample. To explain the reason for this phenomenon, the dynamic kinetic capillary isoelectric focusing (DK-CIEF) approach proposed previously, which allows for the discrimination of different types of protein-DNA interactions and the measurement of the individual dissociation rate constants, was modified and applied to examine possible protein-DNA interactions involved. It was found that a non-specific DNA-protein binding occurs in the sample, the dissociation rate constant for which was measured to be 7.05 ± 0.83 × 10⁻³ s⁻¹. The formation of DNA-protein complex was suggested to be the main reason for the incomplete digestion of the DNA sample. The modified DK-CIEF approach can be applied as general DNA samples, with the advantages of fast speed and low sample consumption.     

测量中的最佳值及标准误差的数学研究

本文对间接测量量的最可信赖值及误差进行推导 ,方法简明 ,计算公式简单 ,学生易接受。     

Refractive index detection in microbore column liquid chromatography

Summary An existing commercial refractive index detector was modified for use with microbore column LC systems. The detector utilizes the Fresnel method. The effect of band dispersion and dilution at the detector side is of extreme importance in connection with the miniaturized LC system. In the modified model the original heat-exchanger tube was removed and a stainless steel capillary was used for heat-exchanging. Gaskets having different cell volumes were also examined with respect to band broadening and sensitivity. The detection limit was 10ng for di-n-pentyl phthalate. The examples include the detection of phthalates, alcohols, n-paraffins, and kerosine.     

Refractive index detection in slurry-packed capillary column LC

An existing commercial refractive index detector was modified for use with slurry-packed capillary column LC systems. The cell gasket of the original detector cell was replaced by a micro cell gasket giving a volume of 0.8 μL. The relationship between detector response and the amount of sample injected was examined. The limit of detection was 2-3 ng for di-n-pentyl phthalate.     

Analysis of a particle method for the one‐dimensional Vlasov‐Maxwell system

In this article we present a particle method for solving numerically the one‐dimensional Vlasov‐Maxwell equations. This method is based on the formulation by characteristics. We perform the error analysis and we investigate the properties of this scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Melting of PbBr2: A DSC investigation

The melting of PbBr₂ in sealed crucibles was investigated by means of DSC. Three factors were considered to affect melting point: i) impurities, ii) the bromine pressure over the PbBr₂, and iii) photolysis. Both crystals and powders were investigated. The peak of the melting changed after sample grinding. The bromine pressure over the PbBr₂ was found to cause a significant error in the determination of the melting point.Lead bromide melts at 370.6±0.2°C. The heat of melting is 42.9±1.8 J g^–1.This revised version was published online in November 2005 with corrections to the Cover Date.     

Geometric Condition Measures and Smoothness Condition Measures for Closed Convex Sets and Linear Regularity of Infinitely Many Closed Convex Sets

In this paper, we study geometric condition measures and smoothness condition measures of closed convex sets, bounded linear regularity, and linear regularity. We show that, under certain conditions, the constant for the linear regularity of infinitely many closed convex sets can be characterized by the geometric condition measure of the intersection or by the smoothness condition measure of the intersection. We study also the bounded linear regularity and present some interesting properties of the general linear regularity problem.The author is grateful to the referees for valuable and constructive suggestions. In particular, she thanks a referee for drawing her attention to Corollary 5.14 of Ref. 3, which inspired her to derive Theorem 4.2 and Corollary 4.2 in the revision of this paper.     

Electrochemical Detection of Anions on an Electrophoresis Microchip with Integrated Silver Electrode

A poly(dimethylsiloxane)/glass hybrid microfluidic chip with integrated silver electrode is described for electrochemical detection of anions. The working electrode was directly fabricated on a glass slide and the chip formed by reversibly sealing of a PDMS slab with microchannels to the slide. Under an alkaline phosphate condition, thiocyanide and three halides were sensitively detected. Factors influencing the separation and detection procedure were discussed and optimized. Linear responses over two magnitudes were obtained with limit of detection at the micromolar level.     

Multiarm star block copolymers via Diels‐Alder click reaction

Two types of multiarm star block copolymers: (polystyrene)_m‐poly(divinylbenzene)‐poly(methyl methacrylate)_n, (PS)_m‐polyDVB‐(PMMA)_n and (polystyrene)_m‐poly(divinylbenzene)‐poly(tert‐butyl acrylate)_k, (PS)_m‐polyDVB‐(PtBA)_k were successfully prepared via a combination of cross‐linking and Diels–Alder click reactions based on “arm‐first” methodology. For this purpose, multiarm star polymer with anthracene functionality as reactive periphery groups was prepared by a cross‐linking reaction of divinyl benzene using α‐anthracene end functionalized polystyrene (PS‐Anth) as a macroinitiator. Thus, obtained multiarm star polymer was then reacted with furan protected maleimide‐end functionalized polymers: PMMA‐MI or PtBA‐MI at reflux temperature of toluene for 48 h resulting in the corresponding multiarm star block copolymers via Diels–Alder click reaction. The multiarm star and multiarm star block copolymers were characterized by using ¹H NMR, SEC, Viscotek triple detection SEC (TD‐SEC) and UV. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 178–187, 2009