The use of APPLE II microcomputer as kinetic laboratory data acquisition system

A laboratory microcomputer system based on an APPLE II microcomputer is presented. Data transfer from a temperature jump equipment or a stopped flow apparatus can be performed via a serial interface, the data can be stored on a memory expansion card or on the disk drives. Data transfer to a central host computer can also be done. Application of the laboratory data system on kinetic and spectroscopic measurements are shown.Dedicated to Prof. Dr.K. L. Komarek on the occasion of his 60th birthday.     

Backward step control for Hilbert space problems

Numerical Algorithms - We analyze backward step control globalization for finding zeros of Gâteaux-differentiable functions that map from a Banach space to a Hilbert space. The results include...     

Band Broadening Function in Size Exclusion Chromatography of Polymers: Review of Some Recent Developments

Summary: This article reviews some recent developments on the determination of the Band Broadening Function (BBF) in Size Exclusion Chromatography (SEC) of polymers. It was carried out in the frame of the IUPAC Project: “Data Treatment in Size Exclusion Chromatography of Polymers”. The correction for band broadening (BB) is important for quantitative determinations of the molar mass distribution (MMD) of narrow-distributed (or highly multimodal) polymers, and of derived variables such as kinetic parameters. In the narrow range of a molar mass standard, the BBF is uniform and of positive skewness. In a broad chromatographic range, the BBF is non-uniform and skewed; and it can be adequately represented by an exponentially-modified Gaussian function (EMG) of 2 parameters that vary slightly with elution volume: an increasing Gaussian variance and a decreasing exponential decay. Additionally, the total BBF variance remains almost constant if not close to the total exclusion limit. The following methods for determining BBF parameters are reviewed: a) a direct method based on assuming Poisson-distributed MMDs; b) a direct method based on measuring the mass- and molar mass chromatograms of narrow standards; c) a theoretical method based on a stochastic model that is equivalent to the Giddings-Eyring model; and d) a theoretical method based on a deterministic model obtained through an extension of the classical van Deemter expression. Ideally, the correction for BB requires a robust numerical inversion algorithm. However, alternative simplified solutions are also possible.     

Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques

In this paper we present a deterministic method for tracing the Pareto frontier in non-linear bi-objective optimization problems with equality and inequality constraints. We reformulate the bi-objective optimization problem as a parametric single-objective optimization problem with an additional Normalized Normal Equality Constraint (NNEC) similar to the existing Normal Boundary Intersection (NBI) and the Normalized Normal Constraint method (NNC). By computing the so called Defining Initial Value Problem (DIVP) for segments of the Pareto front and solving a continuation problem with a standard integrator for ordinary differential equations (ODE) we can trace the Pareto front. We call the resulting approach ODE NNEC method and demonstrate numerically that it can yield the entire Pareto frontier to high accuracy. Moreover, due to event detection capabilities available for common ODE integrators, changes in the active constraints can be automatically detected. The features of the current algorithm are illustrated for two case studies whose Matlab® code is available as Electronic Supplementary Material to this article.     

Correction to: A sequential homotopy method for mathematical programming problems

Mathematical Programming - A correction to this paper has been published: https://doi.org/10.1007/s10107-021-01668-5     

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

Mathematical Programming - We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and...     

Inverse size exclusion chromatography and universal calibration

The mechanism of size-exclusion chromatography (SEC) is reciprocal in respect to the properties of the porous material and of the solutes immersed. The porosimetric interpretation (inverse SEC) yields information about the morphology of porous solids. It depends on a number of assumptions and in particular on the steric properties of the probing macromolecules whose ‘Universal Calibration’ remains disputed to this day. The central question concerns the equilibrium distribution of molecules in confined spaces of complex geometry, and is, as such, not limited to the particulars of chromatographic technique. This survey hopes to help focus future research activities in this field of analytical chemistry and material science.