A new algorithm for minimizing convex functions over convex sets

Let be a convex set for which there is an oracle with the following property. Given any pointz∈ℝ ⁿ the oracle returns a “Yes” ifz∈S; whereas ifz∉S then the oracle returns a “No” together with a hyperplane that separatesz fromS. The feasibility problem is the problem of finding a point inS; the convex optimization problem is the problem of minimizing a convex function overS. We present a new algorithm for the feasibility problem. The notion of a volumetric center of a polytope and a related ellipsoid of maximum volume inscribable in the polytope are central to the algorithm. Our algorithm has a significantly better global convergence rate and time complexity than the ellipsoid algorithm. The algorithm for the feasibility problem easily adapts to the convex optimization problem.     

Influence of static and dynamical structural changes on ultrafast processes mediated by conical intersections

The technological needs imposed by the exponential miniaturization trend of conventional electronic devices has drawn attention towards the development of smaller and faster devices like ultrafast molecular switches. In recent years molecular switches emerge again in the focus of active and innovative research with state-of-the-art optical tools recording their dynamics in real time. Still many questions about the underlying microscopic mechanism are left open, including potential factors that effect the switching process in either way, improve or worsen it. Due to the complexity of such molecules it is difficult to obtain a global answer from experiment alone. On the other side molecular switches are generally too large for a complete quantum chemical and quantum dynamical calculation. In our group we therefore developed an ab initio based modular model to handle the laser induced quantum dynamics in molecular switches like fulgides. It enables us to study the effect of internal molecular coupling and of the molecular response to external fields. We can investigate the related wave packet dynamics, the switching efficiency and the controllability. Our results focus on the laser induced ring opening in fulgides, which equals one direction of the switching process. Presented are the influence of a conical intersection seam and of time-dependent potentials, mimicking the mean interaction with the environment. Furthermore the relation of controllability and the wave packet's momentum is studied and the influence of potential barriers on the switching dynamics is shown.     

Chiral discrimination ofN-(dansyl)-dl-amino acids on human serum albumin stationary phase: Effect of a mobile phase modifier

Summary The effect of perchlorate anion as mobile phase modifier on the separation factor, α, forN-(dansyl)-dl-norvaline andN-(dansyl)-dl-tryptophan on a human serum albumin (HSA) column was studied by varying the concentration,c, of the chaotropic agent and the column temperatureT. Gibbs-Helmholtz parameters Δ(ΔH) and Δ(ΔS) between thed andl enantiomers were determined from linear van't Hoff plots of lnα against 1/T. Thermodynamic results indicated that the enhancement of the separation factor observed asc was increased was enthalpically controlled owing to stereoselective H-bonding interactions. Such behavior was used to optimize the chromatographic conditions for separation ofN-(dansyl)-amino acids on HSA.     

Computer optimization of separation in gas-solid chromatography,optimization model and computer-modified mapping procedure

Summary This paper proposes an optimization model for gas-solid chromatographic separations in a non-linear programming form and an approximate equation of the plate height for the model. A computer-modified mapping procedure is also described for searching the optimum separation conditions. Just five experiments and about 20 minutes of the computer time are needed to establish the optima of column temperature and of the carrier gas linear velocity. The relative deviation between the predicted and the experimental values was found to be within 20% for the plate heights, and within 1.5% for the retention times.     

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.     

Computer-assisted optimization of reversed-phase HPLC isocratic separation of neutral compounds

An appropriate optimization strategy should be used to find a desired resolution or selectivity with a minimum number of experiments in a limited time, which could assure the baseline separation of all target compounds. It was usually realized by means of a specialized computer program. In this paper, mapping optimization method and overlapping resolution mapping were compared for the optimization of a reversed-phase high-performance liquid chromatography (HPLC) isocratic separation of neutral compounds. The calculated resolutions and separation time of 7 to 10 experiments are fitted by different equations, which were used to build a contour plot with a minimum effective resolution and maximum retention time as a function of a mobile phase composition. The balance between resolution and analysis time could be easily realized by the overlapping of the final overlapping resolution mapping and analysis time mapping. The validity of the two methods was confirmed by some typical experiments. The models are simple, visual, and common without theoretical arithmetic.     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

Analysis of long-term distributions of calibration parameters and calibration intervals for an atomic absorption spectrophotometer

 A combination of "black box" and "calendar-time" methods for the determination of calibration intervals of an analytical measuring instrument is discussed. Since the methods require information on the distributions of the calibration parameters, such information is described for an atomic absorption spectrophotometer, as an example. The hypotheses on the normal distribution of the calibration parameters are tested using the ω²-criterion and accepted at 0.90–0.95 levels of confidence. Corresponding control charts are designed for indication of warning and action limits of the calibration parameters, and diagnoses of outliers in further calibrations. Control charts indicate also when the calibration should be done according to the full program of the equipment manufacturer. Received: 15 April 2000 / Accepted: 24 July 2000     

Study of reaction processes by in-line near-infrared spectroscopy in combination with multivariate curve resolution: Esterification of myristic acid with isopropanol

The acid-catalysed esterification of myristic acid with isopropanol was studied by using near-infrared spectroscopy (NIR) in combination with soft-modeling curve resolution (MCR) methodology with a view to establishing the effect of experimental variables on the reaction kinetics. The reaction was conducted at temperatures above the boiling point of the alcohol, with continuous addition of an isopropanol/water mixture to the reactor. Spectral and concentration profiles were determined by applying soft-modeling curve resolution methodology to a column-wise augmented data matrix containing the spectra for the pure components. MCR profiles were compared with reference values and found to depart from then by less than 3% as %RSE for concentrations and to exhibit correlation above 0.999 for spectra.The reaction kinetics as estimated from the concentration profiles was found to be pseudo-first-order. Also, the pseudo-first-order rate constant was found to depend on the flow-rate of the isopropanol/water mixture and its water content; although the constant decreased with increase in the proportion of water, a content of ca. 15% could be used without important retarding effects on the kinetics. The proposed NIR-MCR method allows the rate constant and the influence of the initial water content to be determined with a view to minimizing consumption of the raw materials and optimizing the experimental conditions.     

Optimization of alkali-alkalkine earth cation separation on weak cation-exchangers

Summary The elution behavior of alkali and earth alkaline cations has been studied on a newly synthesized weak cationexchanger (WCX). Applying this stationary phase isocratic separation of these cations is possible. The dependence of retention on competing ion concentration is described via a simple model. The influence of crown ethers as well as organic eluent additives on selectivity and peak efficiency is demonstrated. With optimized separation such cations can be determined with detection limits of about 0.5 ppm using a conductivity detector without ion suppression.