On the conundrum of deriving exact solutions from approximate master equations

We derive the exact time-evolution for a general quantum system under the influence of a bosonic bath that causes pure phase noise and demonstrate that for a Gaussian initial state of the bath, the exact result can be obtained also within a perturbative time-local master equation approach already in second order of the system–bath coupling strength. We reveal that this equivalence holds if the initial state of the bath can be mapped to a Gaussian phase-space distribution function. Moreover, we discuss the relation to the standard Bloch–Redfield approach.     

Logarithmic analysis of two overlapping d.c. polarographic waves: V. Application of a minicomputer to automatic analysis

A system for automatic analysis of d.c. polarographic waves, based on a DEC PDP-11/20 minicomputer and a PAR 170 Electrochemical system is described. More general expressions for analysis and separation of overlapping d.c. polarographic waves are derived than those previously reported in the literature. Corresponding programs are prepared in order to enable the automatic interpretation of polarographic experiments in an on-line system.     

Automatic polarographic elucidation of electrode mechanisms by means of a knowledge-based system : Part 1. Sampled d.c. polarography

A knowledge-based system has been developed for the automatic elucidation of electrochemical mechanisms. The system is based on sampled direct current (or Tast) polarography at a dropping mercury electrode as a technique for collecting experimental information and consists of a general expert system shell for the reasoning process, the specific set of rules and experimental modules. The set of rules allows the elucidation of eight relatively simple electrode reaction mechanisms fully atomatically. The computer system has been validated with chemical systems the electrochemical behaviour of which is well established. All parts of the program are written in FORTH language for Apple II microcomputers. This expert system has an open character and new rules can be added to extend the set of mechanisms that can be determined.     

Spurenanalyse von huminstoffen im trinkwasser: The d.c. polarographic determination of traces of humic substances in potable waters

(The d.c. polarographic determination of traces of humic substances in potable waters) The inhibiting effect of a tri-n-butylphosphate layer adsorbed at the mercury drop on the polarographic wave of copper(II) is reduced by humic substances. This effect can be utilized to determine humic substances in the range 0.05–1 mg l^-1. The standard substance used was isolated from peaty water. Humic and fulvic acids are not differentiated but amino acids, peptides and polyhydroxy compounds do not interfere.     

On the theory of polarographic maxima

The theory of polarographic maxima is presented taking into account the interaction of momentum transport, the electrostatic potential field, the adsorption—desorption and the faradaic processes. Several earlier results are generalised. The systems approach employed here is also extended to quasi-linear situations.     

Enhancement of polarographic reduction currents by a static magnetic field

The effect of a magnetic field on d.c. polarographic reduction currents was studied with a static magnetic field applied perpendicularly to the dropping mercury electrode. In the presence of the magnetic field, diffusion or migration currents show a slight but distinct increase. The factors which can influence this effect have been examined experimentally. The effect is interpreted in terms of suppression of transfer of concentration polarization from one drop to the next. It is shown that certain types of maxima are enhanced by application of a magnetic field.     

Resolution enhancement of a.c. polarographic peaks by deconvolution using the fast fourier transform

A method for resolution enhancement of a.c. polarograms (voltammograms) is presented. The method is based on deconvolution using fast Fourier transforms. Overlapped a.c. polarograms are mathematically narrowed and sharpened, retaining the peak position and linear proportionality of the sharpened peak height with concentration. The advantages and limitations of the method are demonstrated on simulated and experimental a.c. polarograms. The same approach is applicable to related techniques such as. differential pulse and square-wave polarography.     

On approximate analytical solutions of differential equations in enzyme kinetics using homotopy perturbation method

Homotopy perturbation method is used to extend the approximate analytical solutions of non-linear reaction equations describing enzyme kinetics for combinations of parameters for which solutions obtained in previous works are not valid. Also, by constructing a new homotopy, alternative approximate analytical expressions for substrate, substrate-enzyme complex and product concentrations are found. These first-order approximate solutions give more accurate results than the second-order approximations derived in previous works.     

Studies of the cathode layer of a d.c. arc

Some factors which affect the cathode layer of a d.c. arc were investigated. It is shown that: (i) varying concentrations of elements with low ionisation potentials in the sample can markedly affect the distribution of atoms in the cathode layer and hence the detection limits of the technique; (ii) variations in arc current and arc gap have only a small effect on the cathode layer provided that these factors are maintained at values above certain minimum levels; (iii) the use of artifical atmospheres and inhomogeneous magnetic fields generally increase detection limits; (iv) detection limits obtained with samples containing relatively high concentrations of elements with low ionisation potentials can be two or three times better than those obtained with conventional anode evaporation techniques provided wandering of the cathode spot is kept to a minimum, a condition which often cannot be realised in practice.     

On the rotational invariance of the fock equations in indo methods using d functions

The rotational invariance of the Fock equations is investigated. It is demonstrated that the inclusion of d functions requires additional hybrid integrals which do not occur in the original version of INDDO . Calculations are performed with SINDO 1 on binding energies, ionization potentials, and dipole moments to show the differences between the various levels of approximation.     

A.c. polarographic determination of polyethylene glycols — application to analysis of photographic processing solutions

The tensammetric behaviour of several polyethylene glycol (PEG) molecules is described. At neutral pH, PEG gives both a positive and a negative peak. At high pH the positive peak is obscured by the anodic dissolution of mercury and at low pH the negative peak is obscured by the hydrogen evolution reaction. Tensammetry is shown to be applicable to the direct determination of PEG in photographic processing solutions. Despite the complex chemical composition of these solutions the only pre-treatment required was dilution of samples.     

Thermal pinch effect in the argon d.c. plasma

Creation and consequences of the marked thermal pinch in the analytical d.c. plasma (DCP) are investigated. The flowing plasma constricts due to interaction between forced convective cooling and electric current regulation of the low power arc. Distinctive visual, spectroscopic and operational features of the DCP are associated with the thermal pinch and the transport properties of hot argon. Response of modelled electron density to changes in cooling gas flow rates are compared to experimental data. Implications for non-local thermodynamic equilibrium (LTE) spectrochemical excitation are noted.     

Rotating electrode d.c. solution conductivity device

In an electrochemical cell with one electrode rotating asymmetrically with respect to a second fixed electrode, a constant current produces an a.c. component of the voltage between the pair at the rotational frequency. This a.c. signal arises from the varying iR drop between the extremes of rotational position and thus is a measure of the conductivity of the cell electrolyte. When such a rotating electrode is added to an operating two-electrode cell (e.g. a plating bath), the a.c. signal derived from the rotating element may be used additionally to map the spatial current distribution in the cell. The filtered and amplified signal in either system has also been used to trigger a counter for digital measurement of electrode rotational speed.