“以直代曲”论

曾盛传数学分析基础教学中对极限的推导有循环论证。这可非同小可。亦曾有人设法补救。能补救吗?要补救吗?究竟是怎么回事?请看——     

富勒烯衍生物的红光光限幅实验

应用钛宝石可调谐脉冲激光,在波长为691nm、脉冲宽度为10ns的条件下,研究了新型富勒烯叠氮乙酰氨衍生物(N-acetamide1,2-dihydro-1,2-azafulerene[60])的光限幅特性。     

HBF4·DEE-catalyzed formation of sulfinyl imines: Synthesis and mechanistic studies

A mild acid-catalysed method is reported for the formation of sulfinyl imines from tert-butanesulfinamide and aromatic or aliphatic aldehydes using tetrafluoroboric acid diethyletherate (10?mol%) in dichloromethane. Reactions were performed at room temperature and gave the corresponding sulfinyl imines in excellent yield after 2?h. A DFT study was performed and a mechanism for the reaction is postulated.     

Three-way Resolution of the Overlapping Ultrahigh-performance Liquid Spectrochromatograms for the Analysis of a Quaternary Mixture Using Parallel Factor Analysis

This paper presents a new application of three-way parallel factor analysis (3W-PARAFAC) model to the coeluting spectrochromatograms for the quantitative resolution of a quaternary mixture system consisting of paracetamol, propyphenazone, and caffeine with aspirin as an internal standard. Spectrochromatograms of calibration standards, validation sets, and unknown samples were recorded as a function of retention time and wavelength in the range of 0.0–2.5?min and 200–400?nm, respectively, using ultra-performance liquid chromatography with photodiode array detection (UPLC-PDA). Three-way UPLC-PDA data array X (retention time?×?wavelength?×?sample) was obtained from the data matrices of the spectrochromatograms. 3W-PARAFAC decomposition of three-way UPLC-PDA data array provided three loading matrices corresponding to chromatographic mode, spectral mode, and relative concentration mode. Quantitative estimation of paracetamol, propyphenazone, and caffeine in analyzed samples was accomplished using the relative concentration mode obtained by the deconvolution of the UPLC-PDA data set. The validity and ability of 3W-PARAFAC model were checked by analyzing independent test samples. It was observed from analyses that 3W-PARAFAC method has potential to uniquely resolve strongly overlapping peaks of analyzed compounds in a spectrochromatogram, which was obtained under experimental conditions consisting of the lower flow rate, short run time, and simple mobile phase composition. The proposed three-way chemometric approach was successfully applied to the simultaneous quantification of paracetamol, propyphenazone, and caffeine in tablets. Experiments showed that the determination results were in good agreement with label amount in commercial pharmaceutical preparation.     

On a theorem of J. Vukman

Summary LetR be a ring. A bi-additive symmetric mappingD:R × R R is called a symmetric bi-derivation if, for any fixedy R, the mappingx D(x, y) is a derivation. J. Vukman [2, Theorem 2] proved that, ifR is a non-commutative prime ring of characteristic not two and three, and ifD:R × R R is a symmetric bi-derivation such that [D(x, x), x] lies in the center ofR for allx R, thenD = 0. This result is in the spirit of the well-known theorem of Posner [1, Theorem 2], which states that the existence of a nonzero derivationd on a prime ringR, such that [d(x), x] lies in the center ofR for allx R, forcesR to be commutative. In this paper we generalize the result of J. Vukman mentioned above to nonzero two-sided ideals of prime rings of characteristic not two and we prove the following. Theorem.Let R be a non-commutative prime ring of characteristic different from two, and I a nonzero two-sided ideal of R. Let D: R × R R be a symmetric bi-derivation. If [D(x, x), x] lies in the center of R for all x I, then D = 0.     

Application of Multivariate Calibration Techniques to HPLC Data for Quantitative Analysis of a Binary Mixture of Hydrochlorathiazide and Losartan in Tablets

New multivariate approaches have been applied to high-performance liquid chromatography (HPLC) with multiwavelength photodiode-array (PDA) detection. Multivariate calibration techniques such as partial least squares (PLS), principal component regression (PCR), classical least squares (CLS), and inverse least squares (ILS) was subjected to HPLC data for simultaneous quantitative analysis of synthetic binary mixtures and a commercial tablet formulation containing hydrochlorothiazide (HCT) and losartan potassium (LST). The combined use of HPLC and multivariate calibrations has been denoted HPLC–CLS, HPLC–ILS, HPLC–PCR, and HPLC–PLS. Successful chromatographic separation of the two active compounds and enalapril maleate, used as internal standard (IS), was accomplished by means of a 4.6 mm i.d. × 250 mm, 5 m particle, Waters Symmetry C₁₈ reversed-phase column and a mobile phase consisting of 60:40 acetate buffer (0.2 M, pH 4.8)–acetonitrile (v/v, 60:40). HPLC data based on the ratio of analyte peak areas to IS peak area were obtained by PDA detection at five-wavelengths (250, 255, 260, 265, and 270 nm). The HPLC–CLS, HPLC–ILS, HPLC–PCR, and HPLC–PLS calibration plots for hydrochlorothiazide and losartan potassium were constructed separately by using the peak-area ratios corresponding to the concentrations of each active compound. The HPLC multivariate calibrations obtained were tested for different synthetic mixtures containing HCT and LST in the presence of the IS. These multivariate chromatographic methods were also applied to a commercial pharmaceutical dosage form containing HCT and LST. The results obtained from the multivariate calibrations were compared with those obtained by use of another, classical HPLC method using single-wavelength detection.Revised: 29 September 2004 and 4 January 2005     

Oxidation of l-methionine with aqueous chromic acid: a kinetic study

The kinetics of oxidation of l-methionine by chromic acid in acidic medium (pH=0.83–2.2) has been studied spectrophotometrically. The effect of l-methionine and chromium(VI) concentrations on the rate of the reaction was determined. The reaction rate decreases with increasing the pH of the medium. The kinetics of the formation of a chromium(III) complex conform to the rate law:with k1=7.5×10–2s–1 and Kes1=43.85 at constant [H+]=1.9×10–2moldm–3 and [l-methionine]T= 2.0×10–2moldm–3. The same values were found with [l-methionine]T variation at constant [H+]. The reaction proceeds through formation of chromium(VI)-l-methionine ester in a rapid pre-equilibrium step, followed by a slower redox reaction of the ester. The present study provides kinetic evidence for formation of a complex ion (ester). One mole of Cr2O72– oxidizes four moles of l-methionine, which acts as a monodentate ligand and binds to chromium(VI) through the sulfur atom. The coordinated sulfur atom of l-methionine–chromium(VI) ester is responsible for the oxidative degradation (breaking of the C1-C2 bond) of l-methionine. Coordinated oxygen of the carboxylate group inhibits the cleavage of the C1-C2 bond.     

Studies on the pitting corrosion of zinc in aqueous solutions II. Measurement of pitting corrosion currents operating under natural conditions

A simple experimental arrangement was applied for the measurement and the evaluation of pitting corrosion currents operating under natural conditions. The feasibility of the procedure was examined by using Zn as a test metal, K₂CrO₄, Na₂HPO₄ and Na₂WO₄ as inhibitors, and Cl^?, Br^? and I^? as pitting corrosion agents. Both the type and concentration of the inhibiting and corroding agents were varied in a programmed manner. In CrO₄^2? and HPO₄^2? solutions, the pitting corrosion currents started to flow after an induction period, which decreased with increase in the concentration of the attacking agent. In WO₄^2? solutions, on the other hand, initially high currents were recorded due to the reduction of the agent to soluble, non-inhibiting species.In all solutions tested the corrosion current reached steady-state values which depended on the type and concentration of both the inhibiting and the aggressive anions. When keeping the inhibitor concentration constant, the corrosion current varied with the concentration of the aggressor according to: log i_corr = a₁ + b₁ log c_agg On the other hand, in solutions of constant aggressor concentration, with varying inhibitor amounts, the relation was: log i_corr = a₂ ? b₂ log c_inh where a₁(a₂) and b₁(b₂) are constants.The two equations were derived theoretically on the basis of competitive adsorption of the two counteracting agents on the surface of the metal. Comparison between the experimental values of a and b, with the corresponding terms of the theoretical equations was made.The aggressivity of the three tested anions decreases in the order Cl^? > Br^? > I^?, whilst inhibition varied as CrO₄^2? > HPO₄^2? > WO₄^2?.