Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

A simple and green procedure for the conjugate addition of thiols to conjugated alkenes employing polyethylene glycol (PEG) as an efficient recyclable medium

Polyethylene glycol (PEG) is found to be an inexpensive, nontoxic, environmentally friendly reaction medium for the conjugate addition of thiols to conjugated alkenes to afford the corresponding adducts in excellent yields under mild and neutral conditions. Products of undesirable side reactions resulting from polymerization are not observed. The use of PEG avoids the use of either acid or base catalysts for this conversion and moreover PEG can be recovered and reused.     

Use of short columns and high flow rates for rapid gradient reversed-phase chromatography

Summary Rapid analyses were performed using reversed-phase liquid chromatography with short (20–100 mm) columns swept by fast yet shallow gradients, and the results compared with those obtained with 150 mm columns and slow gradients. The resolution losses incurred with shorter columns were minimised by employing elevated flow rates, to ensure that comparable mean retention factors were experienced by individual analytes during gradients run on different columns. This conserves gradient steepness. High quality performance was obtained with turn-around times of 5–10 minutes. An overall 5-fold enhancement in the rate of information generation was obtained. The relevance of instrumental parameters and of column and packing dimensions, upon the potential for improved performance is discussed. Some implications for the rapidly developing technique of capillary electrochromatography are briefly indicated.     

Computerized optimization of gradient elution conditions with ternary solvent mobile phases in RPLC

Summary In this work, an optimization procedure for gradient RPLC separation, using ternary mobile phases, is described. This procedure requires eight preliminary experiments in gradient elution mode to predict the retention surface for each solute over the whole triangular space. This is followed by computerized calculations to determine the best ternary gradient elution profile with respect to both selectivity and analysis time. The efficiency of this procedure from the point of view of rapidity and of accuracy, is illustrated for the specific separation of twelve phenyl urea herbicides.     

A novel synthesis, including asymmetric synthesis, of 2,4,4-trisubstituted 2-cyclopentenones based on the reaction of 1-chlorovinyl p-tolyl sulfoxides with acetonitrile and its homologues

Reaction of 1-chlorovinyl p-tolyl sulfoxides, which were synthesized from chloromethyl p-tolyl sulfoxide and ketones in high overall yields, with cyanomethyllithium (lithium α-carbanion of acetonitrile) gave adducts in high to quantitative yields. The adducts were treated with LDA followed by lithium α-carbanion of the homologues of acetonitrile to give 3,5,5-trisubstituted enaminonitriles in good to high yields. Hydrolysis of the enaminonitriles under acidic conditions gave 2,4,4-trisubstituted 2-cyclopentenones in good yields. By using the optically active chloromethyl p-tolyl sulfoxide and unsymmetrical ketones, this procedure gave the optically pure 2,4,4-trisubstituted 2-cyclopentenones. The scope and limitations of this method and the mechanism of the reactions are also discussed. These procedures offer a new and effective method for the synthesis of 2,4,4-trisubstituted 2-cyclopentenones from four components, ketones, chloromethyl p-tolyl sulfoxide, acetonitrile, and its homologues.     

Highly diastereoselective conjugate additions of monoorganocopper reagents to chiral imides

Stereoselective conjugate additions to chiral N-enoyl amides employing various monoorganocuprate reagents, Li[RCuI], are described. The presence of TMSI in the addition of Li[RCuI] in THF provided the highest stereoselectivities. Reversed major diastereomeric ratios were obtained employing Li[RCuI] in ether or conventional copper-promoted Grignard reagents. The results presented support the favored anti-s-cis conformation of the substrates using Li[RCuI]/TMSI in THF, while the copper-promoted Grignard reagents or the Li[RCuI] reagents in ether favor the opposite syn-s-cis conformation. Influence of lithium ions on the stereoselective conjugate addition of the monoorganocuprate reagent, Li[BuCuI], has been investigated and two different mechanistic pathways are presented. The results show that iodotrimethylsilane (TMSI) is crucial for the asymmetric conjugate addition of the copper reagent, but only in THF or when 12-crown-4 is used. The reaction is thought not to involve any halosilane in any critical steps in the organocopper mechanisms conducted in ether. The (CuI)₄(SMe₂)₃ complex precursor plays an instrumental role for the conjugate addition using monoorganocopper reagents.     

Conjugate base catalysed one-pot synthesis of pyrazoles from β-formyl enamides

A novel one-pot synthesis of pyrazoles has been accomplished by the reaction of β-formyl enamides with hydroxylamine hydrochloride catalysed by potassium dihydrogenphosphate in acid medium.     

Effect of mobile phase density gradients on efficiency in packed column supercritical fluid chromatography

Summary The efficiency of packed columns was measured as a function of flow rate, temperature, outlet density, and the density differential across the column, unsing pure carbon dioxide as the mobile phase. Although density differentials are often blamed for a serious loss in efficiency in packed column supercritical fluid chromatography, the results show that efficiency was not a function of the density differential. Peak shapes suggest that apparent loss in efficiency is actually due to inadequate solubility of the solute in carbon dioxide.     

Performance characteristics of suspended particulate reagent-iminodiacetate as a binding agent for diffusive gradients in thin films

The performance characteristics of an alternative binding agent, suspended particulate reagent-iminodiacetate (SPR-IDA), for use with DGT methodology were investigated. The parameters investigated during this study included gel hydration, blank levels, elution factor (f_e), capacity, the effects of pH on the binding of trace metals by DGT. The novel application of this resin for use as a quantitative standard for laser ablation ICP-MS was also evaluated. To further constrain the results for the SPR-IDA binding agent, parallel experiments were performed using resin gel containing Chelex 100, which has been widely reported in the literature. Hydration results showed that the SPR-IDA resin gel reached a stable dimension and weight within ∼30 min and was dimensionally stable for ≤6 months. The measured DGT blanks for the SPR-IDA resin were 0.0023, 0.15, 0.21, 0.0033 and 0.011 ng disc⁻¹ for Co, Ni, Cu, Cd and Pb, respectively. The elution factor differed for the two resin types with the Chelex 100 recoveries slightly lower than previous reports and the SPR-IDA resin showing on average ∼5-9% better recoveries than DGT containing Chelex 100. The measured capacity of DGT discs containing the SPR-IDA binding agent was 0.26 mg Cd, similar to the calculated value of 0.29 mg Cd, indicating the entire resin layer was available for metal uptake.Both resin types performed equally well when deployed in 1 mM NaNO₃ solutions with DGT measurements of ∼100% of direct solution measurements for Co, Ni and Cd. However, DGT measurements of Cu and Pb systematically decreased with increasing solution pH down to ∼50% of solution values at pH 8.0, due to artifacts resulting from colloid formation during the addition of the metals. This was remedied by adding the metals as dilute salt standards and addition of Mg(NO₃)₂ to eliminate adsorption to the container walls. In the latter experiments, DGT measured concentrations of Co, Ni, Cu, Cd and Pb were in agreement with solution concentrations. Deployment of DGT in solutions with increasing concentrations of trace metals yielded linear results, suggesting that quantitative analysis using simplified laser ablation techniques should be possible using this newly characterized SPR-IDA resin gel.     

单双层共轭系统的共轭高度对等晕角的影响

 简要介绍了传统自适应光学系统的局限性和多层共轭自适应光学基本原理。模拟了单双层共轭校正系统的共轭高度,并结合平程与垂程(HV模型)两种传输状态对系统等晕角增益作了进一步的分析。对单层共轭系统,在20 km的传输距离内,在平程中整个区域都属于等晕角放大区,共轭高度的最佳位置在传输距离的中间（约10 km处）,等晕角取极大值,增益效果较好;但垂程中增益效果变差,且等晕角放大区也仅在3.6 km之内。对双层共轭系统来说,第1层共轭高度的变形镜主要对近距离畸变波前进行校正,并对整个传输距离的等晕角影响很大,是双层共轭系统的关键因素;第2层共轭高度对远距离等晕角影响较大。