Retention modeling and simultaneous optimization of pH value and gradient steepness in RP‐HPLC using feed‐forward neural networks

A novel approach is proposed for the simultaneous optimization of mobile phase pH and gradient steepness in RP‐HPLC using artificial neural networks. By presetting the initial and final concentration of the organic solvent, a limited number of experiments with different gradient time and pH value of mobile phase are arranged in the two‐dimensional space of mobile phase parameters. The retention behavior of each solute is modeled using an individual artificial neural network. An “early stopping” strategy is adopted to ensure the predicting capability of neural networks. The trained neural networks can be used to predict the retention time of solutes under arbitrary mobile phase conditions in the optimization region. Finally, the optimal separation conditions can be found according to a global resolution function. The effectiveness of this method is validated by optimization of separation conditions for amino acids derivatised by a new fluorescent reagent.     

Variational transition state theory without the minimum-energy path

In this paper we propose a method for carrying out variational transition state theory calculations without first obtaining a converged minimum-energy path (MEP). We illustrate the method in two ways, first of all by employing an unconverged MEP and secondly by using a dynamically optimized distinguished reaction path. Preliminary tests of the algorithm for the reactions OH+H₂→H₂O+H and C₂H₅→C₂H₄+H are very encouraging. Received: 22 January 1997 / Accepted: 11 March 1997     

Sequential optimisation of the separation of a complex mixture of plastics additives by HPLC with a quaternary gradient and a dual detection system

Summary The separation of two families of plastics additives (phenolic antioxidants and UV absorbers) has been achieved by high performance liquid chromatography with a quaternary gradient. A methodology of separation based on a sequential optimization is described. After a preliminary study of the effects of solvents on retention of compounds, the mobile phase is first chosen for each class of additives (Irganox and Tinuvin), then for the mixture of all the compounds and the separation is finally optimized. The importance of the column phase ratio is also reported. The use of two detectors, UV absorbance and light-scattering, enables all the compounds to be detected. The performance of the detectors has been compared and the effects of the nebulization temperature on the detection of low molecular mass compounds is reported.     

GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat

In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS.We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%.We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.     

Structural optimization with parameter-transfer finite element

A mathematical method to solve structural problems, using parameter-transfer finite elements (P-TFE) was recently proposed by the authors [1] [2] [3]. The proposed transfer finite element approach is able to create a mathematical model of a structure, taking into account directly the whole behaviour of the structure under dynamic, aerodynamic, and thermal actions, and not by assembling, in a separate fashion, the stiffness and the mass matrix on one side and the external load vector as performed by the classical finite element procedure.The purpose of this paper is to apply the above methodology to optimization problems, in particular to obtain the minimum structural weight for a beam, under primary constraints on buckling load or natural frequencies.The use of P-TFE in the field of structural optimization overcomes most difficulties of the usual techniques of solution and the element is particularly useful in the evaluation of the sensitivity matrix.The formulation of the optimization problem based on P-TFE is presented and some applications are studied. The numerical results obtained are compared with other existing methodologies and briefly discussed.

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Sommario Gli autori hanno già proposto un metodo per studiare problemi strutturali [1] [2] [3], introducendo una nuova metodologia di discretizzazione, basata sull'impiego di elementi finiti di trasferimento, funzioni esplicite di un parametro, indicati come P-TFE. Tali elementi sono in grado di rappresentare, in similitudine alla funzione di trasferimento, il comportamento completo dell'elemento strutturale in esame, soggetto ad azioni dinamiche, aerodinamiche e termiche; sono parimenti in grado di produrre, in similitudine al metodo degli elementi finiti, un modello matematico discreto di un continuo.Scopo del presente lavoro è di applicare detta metodologia a problemi di ottimizzazione, in particolare alla ricerca del minimo peso per una trave che mantenga inalterate le sue caratteristiche di carico critico o le frequenze naturali di vibrazione.Vengono quindi presentati alcuni risultati numerici dei casi esaminati e confrontati con quelli ottenuti da altri autori con l'impiego di altre metodologie.

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List of Symbols {B} _m vector of the generalized state variables - {C} _m vector of integration constants - [I] unit matrix - EI bending stiffness - A cross-sectional area - u adimensional thickness - l beam length - M,M bending moment - [N] _m shape function ofm-th order - [N*] shape function atx ₀ - P axial load - [R] _i transfer matrix of thei-th element - T,T shear force - w transverse displacement - x adimensional independent variable - x ₀ value ofx at the left of the element - {Y} vector of state variables - {Y*} imposed condition atx ₀ - _0m Kronecker delta with the first pedix always set equal to zero - normalized eigenfrequency - normalized buckling load - mass density     

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.     

Copolymers of methyl methacrylate with some benzanthrone dyes, photo-stabilisers and their combined structures

Copolymerisation of methyl methacrylate with nine novel monomer compounds, triazinyl benzanthrone dyes, triazinyl benzotriazole stabilisers and their combined structures, was investigated. Chemical bonding of the compounds in the polymers obtained was confirmed spectrophotometrically. The quantity of the chemically bonded monomer compounds was determined to be over 50%, providing a colour and a fluorescence stable to solvents. Their influence on the rate of the copolymerisation was studied. It was found that the compounds under study did not significantly affect the rate of copolymerisation. A stabilizing effect towards photo-degradation of PMMA was achieved at 0.1 wt.% initial concentration of the compounds, which made them suitable for “one-step” colouration and stabilisation of PMMA.     

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.