A new method of moving asymptotes for large-scale linearly equality-constrained minimization

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems.     

L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.     

Solid phase analytical derivatization of anthropogenic and natural phenolic estrogen mimics with pentafluoropyridine for gas chromatography-mass spectrometry

A simple, low cost, fast and sensitive method is reported for the determination of the four endocrine disrupting chemicals (EDCs) 4-tert-butylphenol, 4-tert-octylphenol, bisphenol A and 17β-estradiol using pentafluoropyridine as the derivatizing reagent. These EDCs were determined by simultaneous extraction and derivatization in a solid phase analytical derivatization (SPAD) technique without the aid of any phase transfer catalyst (PTC) or an ion-pair mechanism. Recoveries of analytes as their tetrafluoropyridyl derivatives from water ranged from 71% for 4-tert-butylphenol to 106% for 17β-estradiol; from urine they ranged from 61% for 17β-estradiol to 91% for 4-tert-octylphenol; and from humic acids solution the ranged from 59% for 17β-estradiol to 104% for 4-tert-octylphenol in humic acid solutions. Calibration curves were constructed from a matrix of human male urine in the range 1-40 ng/mL and had coefficients of correlation greater than 0.99. For 4-tert-butylphenol, bisphenol A and 17β-estradiol the limits of quantitation were 5 ng/mL and for 4-tert-octylphenol it was 1 ng/mL. This method was applied to determine EDCs and detected 4-tert-octylphenol, bisphenol A and 17β-estradiol in concentrations comparable to those found in the literature. The method offers advantages in speed of analysis, reduced reagent and specificity of derivatization.     

Macroscopic investigation of the transient hydrodynamic memory behavior of preparative packed chromatography beds

The goal of the present work was to examine the hydrodynamic behavior of preparative scale packed chromatography beds during long-term cyclical operation at high loads using an experimental set-up with a high resolution measuring device of bed height. One agarose-based resin and one methacrylic-based resin were examined in a 140 mm column. Both resins exhibited hysteresis behavior during compression/relaxation cycles. The hystereses were less pronounced with decreasing hydrodynamic stress rate. The occurrence of hystereses was an indication for hydrodynamic memory behavior of the chromatography packing. During long-term cyclical operation at high loads of the column filled with methacrylic resin, oscillations of the steadily with time decreasing flow rate were observed for the first time. These oscillations were attributed to the viscoelasticity of the polymer particles network representing a system with materials with fading memory. Such nonlinear systems with feed-back are known to exhibit inherent self-oscillations. A decoupling of the two processes of bed compression and decrease of bed permeability was observed. The presented results explain why preparative packed-bed chromatography often yields unsatisfactory reproducible data and why unwanted phenomena like medium wall detachment or other symptoms of deteriorated chromatography beds are frequently observed.     

Quantifying temperature and flow rate effects on the performance of a fixed-bed chromatographic reactor

Chromatographic reactors are based on coupling chemical reactions with chromatographic separation in fixed-beds. Temperature and flow rate are important parameters for the performance of such reactors. Temperature affects mainly adsorption, chemical equilibria, mass transfer and reaction kinetics, whereas flow rate influences residence time and dispersion. In order to evaluate the mentioned effects, the hydrolysis reactions of methyl formate (MF) and methyl acetate (MA) were chosen as case studies. These reactions were performed experimentally in a lab-scale fixed-bed chromatographic reactor packed with a strong acidic ion exchange resin. The chosen reactions can be considered to represent a relative fast (MF) and a relative slow (MA) reaction. The processes which take place inside the reactor were described and simulated using an isothermal equilibrium dispersive model. The essential model parameters were determined experimentally at different temperatures and flow rates. The performance of the chromatographic reactor was evaluated at several discrete constant temperature levels by quantifying product purity, productivity and yield. The work provides insight regarding the influence of temperature and flow rate on values of the model parameters and the performance criteria.     

Kinetic performance limits of constant pressure versus constant flow rate gradient elution separations. Part I: theory

We report on a general theoretical assessment of the potential kinetic advantages of running LC gradient elution separations in the constant-pressure mode instead of in the customarily used constant-flow rate mode. Analytical calculations as well as numerical simulation results are presented. It is shown that, provided both modes are run with the same volume-based gradient program, the constant-pressure mode can potentially offer an identical separation selectivity (except from some small differences induced by the difference in pressure and viscous heating trajectory), but in a significantly shorter time. For a gradient running between 5 and 95% of organic modifier, the decrease in analysis time can be expected to be of the order of some 20% for both water–methanol and water–acetonitrile gradients, and only weakly depending on the value of V_G/V₀ (or equivalently t_G/t₀). Obviously, the gain will be smaller when the start and end composition lie closer to the viscosity maximum of the considered water-organic modifier system. The assumptions underlying the obtained results (no effects of pressure and temperature on the viscosity or retention coefficient) are critically reviewed, and can be inferred to only have a small effect on the general conclusions. It is also shown that, under the adopted assumptions, the kinetic plot theory also holds for operations where the flow rate varies with the time, as is the case for constant-pressure operation. Comparing both operation modes in a kinetic plot representing the maximal peak capacity versus time, it is theoretically predicted here that both modes can be expected to perform equally well in the fully C-term dominated regime (where H varies linearly with the flow rate), while the constant pressure mode is advantageous for all lower flow rates. Near the optimal flow rate, and for linear gradients running from 5 to 95% organic modifier, time gains of the order of some 20% can be expected (or 25–30% when accounting for the fact that the constant pressure mode can be run without having to leave a pressure safety margin of 5–10% as is needed in the constant flow rate mode).     

Size and diffusion effects on the oxidation of formic acid and ethanol on platinum nanoparticles

Formic acid and ethanol oxidations on spherical platinum nanoparticles dispersed on carbon with different loadings have been studied. The increasing loading of the catalyst leads to a lower diffusion flux of reactants in the internal parts of the catalyst layer, resulting in a lower apparent activity. In some cases, as in ethanol oxidation, it may also affect the diffusion of the products. As a practical consequence, the structure of the supporting layer and the catalyst loading should be optimized so that the maximum catalyst utilization is obtained. Finally, these diffusion effects may mask some important catalytic activity increase of the nanoparticles. In the case of formic acid, a significant increase in the activity is obtained for very small nanoparticles.