A remark on the Riemann‐Hilbert problem with a vanishing coefficient

This paper concerns the existence of nontrivial solutions of the Riemann‐Hilbert problem with a continuous coefficient whose values belong to two rays in the complex plane. Our results extend those recently obtained by E. Shargorodsky and J. F. Toland [6]. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear advertising capital model with time delayed feedback between advertising and stock of goodwill

According to the classical Nerlove-Arrow model, advertising expenditure can be considered as a capital investment to create present and future demand for the firm's products and, hence, to create present and future revenues for the firm. Advertising is assumed to influence via stock of goodwill which cumulatively counts for the effects of the firm's current and past advertising outlays. The paper presents a time delayed feedback model describing the relations between advertising and goodwill. Three different types of effects of advertising upon the dynamics of goodwill are modelled. The advertising policy of the management is incorporated into the model via a non-linear advertising function. The advertising function controls the advertising outlay e.g. by budget constraint and by the actual and target values of goodwill. The behavior of the model is analysed both analytically and numerically. Special attention is given for deriving the stability conditions for the limiting solution. The cases of repelling or chaotic limiting solutions are analysed by bifurcation and state space diagrams. Several numerical examples are given.     

Determination of clodronate in aqueous solutions by HPLC using postcolumn derivatisation

A method for the determination of clodronate at ppm levels in aqueous solutions by HPLC is presented. Clodronate is first separated by anion exchange chromatography using a solution of nitric acid and sodium nitrate as eluent. Th-EDTA-XO mixed ligand complex is used as a postcolumn reagent for clodronate. Clodronate reacts quantitatively with this complex in slightly acid solutions, and a change in the absorbance of Th-EDTA-XO is used as a measure for the clodronate concentration. The detection limit is about 3 ppm, and the linear dynamic range of the method extends up to about 200 ppm. The RSD values varied between 5 and 16%. The effect of pH on appearance and retention of different forms of clodronate is studied. Different forms of clodronate can be separated and detected in the used anion-exchange system.     

Kinetics of bioconjugate nanoparticle label binding in a sandwich-type immunoassay

Nanoparticle labels have enhanced the performance of diagnostic, screening, and other measurement applications and hold further promise for more sensitive, precise, and cost-effective assay technologies. Nevertheless, a clear view of the biomolecular interactions on the molecular level is missing. Controlling the ratio of molecular recognition over undesired nonspecific adhesion is the key to improve biosensing with nanoparticles. To improve this ratio with an aim to disallow nonspecific binding, a more detailed perspective into the kinetic differences between the cases is needed. We present the application of two novel methods to determine complex binding kinetics of bioconjugate nanoparticles, interferometry, and force spectroscopy. Force spectroscopy is an atomic force microscopy technique and optical interferometry is a direct method to monitor reaction kinetics in second-hour timescale, both having steadily increasing importance in nanomedicine. The combination is perfectly suited for this purpose, due to the high sensitivity to detect binding events and the ability to investigate biological samples under physiological conditions. We have attached a single biofunctionalized nanoparticle to the outer tip apex and studied the binding behavior of the nanoparticle in a sandwich-type immunoassay using dynamic force spectroscopy in millisecond timescale. Utilization of the two novel methods allowed characterization of binding kinetics in a time range spanning from 50 ms to 4 h. These experiments allowed detection and demonstration of differences between specific and nonspecific binding. Most importantly, nonspecific binding of a nanoparticle was reduced at contact times below 100 ms with the solid-phase surface.

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Figure A single biofunctionalized nanoparticle was attached to the outer tip apex and the binding behavior of the nanoparticle in a sandwich-type immunoassay, A) without analyte, B) with analyte and C) saturating analyte concentration, was recorded using dynamic force spectroscopy in millisecond timescale. The setting allowed measurement of the association speed of nonspecific binding.

     

Kinetics and particle size control in non-stirred precipitation polymerization of N-isopropylacrylamide

A novel non-stirred precipitation polymerization for rapid small-scale synthesis of monodisperse temperature-sensitive poly(N-isopropylacrylamide) microgels is introduced. A practical framework for the final particle size control is established, and low-temperature synthesis is highlighted as an easy alternative for producing large particles in contrast to the temperature ramp method. Furthermore, in situ 3D-DLS method is used to determine the kinetic rate law of the precipitation polymerization of N-isopropylacrylamide. The power law exponents for the reaction are determined to be 0.97?±?0.12 and 0.46?±?0.01 for the monomer and the initiator concentration, respectively. In conjunction with other evidence, it is suggested that the reaction follows conventional radical polymerization kinetics and takes place in the continuous phase. Number concentration of particles in the batch is recognized to be the determining factor for the final particle volume of the microgels.     

Contribution to the study of complexing properties of Zn-metallothioneins by CZE-DAD

The complexing properties of the sub-isoforms of several mammalian Zn-containing metallothioneins (ZnMT) from different origins (rat, rabbit and human foetal livers) have been investigated by capillary zone electrophoresis coupled to diode array detection (CZE-DAD). MTs were submitted to three different experiments: gradual additions of Cd to MT at pH 8.0, variation of the pH and addition of Cd followed by a variation of the pH. On the whole there seems to be no displacement of the zinc originally present in the MT, but incorporation of Cd in the molecule in order to reach saturation. Furthermore, the pH variations allow one to conclude a certain reversibility of the system. All these results confirm those previously obtained by differential pulse polarography (DPP). The procedure used in this work shows that the sub-isoforms of an MT may exhibit variable complexing properties. This is particularly well illustrated in the case of rat liver MT-2. Much likely there are different mixed complexes of Cd and Zn in each sub-isoform, forming various metalloforms. This work illustrates a different and original use of CZE-DAD for studying the complexing properties of metal-binding proteins.