The purpose of this study was to investigate the fundamental characteristics of a chelating surfactant in terms of solution behaviour, chelation of divalent metal ions, and interaction in mixtures with different foaming agents and divalent metal ion, as well as examining its prospects in some practical applications. Chelating surfactants are functional molecules, with both surface active and chelating properties, which are water soluble and therefore suitable for chelation in many aqueous environments. The dual functionality offers the possibility to recover the chelating surfactant as well as the metals. The DTPA (diethylenetriaminepentaacetic acid)-based chelating surfactant 4-C12-DTPA (2-dodecyldiethylenetriaminepentaacetic acid) was synthesized at Mid Sweden University. In the absence of metal ions, all eight donor atoms in the headgroup of 4-C12-DTPA are titrating and the headgroup charge can be tuned from +3 to -5 by altering the pH. The solution properties, studied by surface tension measurements and NMR diffusometry, were consequently found strongly pH dependent. pH measurements of chelating surfactant solutions as a function of concentration was used to extract information regarding the interaction between surfactants in the aggregation process. Small differences in the conditional stability constants (log K) between coordination complexes of DTPA and 4-C12-DTPA, determined by competition measurements utilizing electrospray ionization mass spectrometry (ESI-MS), indicated that the hydrocarbon tail only affected the chelating ability of the headgroup to a limited extent. This was further confirmed in hydrogen peroxide bleaching of thermomechanical pulp (TMP) treated with 4-C12-DTPA. Interaction parameters for mixed systems of 4-C12-DTPA and different foaming agents were calculated following the approach of Rubingh’s regular solution theory. The mixtures were also examined with addition of divalent metal ions in equimolar ratio to the chelating surfactant. Strong correlation was found between the interaction parameter and the phase transfer efficiency of Ni2+ ions during flotations. Furthermore, a significant difference in log K between different metal complexes with 4-C12-DTPA enabled selective recovery of the metal ion with the highest log K. The findings in this study contribute to the understanding of the fundamental characteristics of chelating surfactants, which can be further utilized in practical applications.

We prove some sufficient conditions for obtaining convergence rates in regularization of linear ill-posed problems in a Hilbert space setting and show that these conditions are directly related with the conditional stability in several concrete inverse problems for partial differential equations.

We prove some sufficient conditions for obtaining convergence rates in regularization of linear ill-posed problems in a Hilbert space setting and show that these conditions are directly related with the conditional stability in several concrete inverse problems for partial differential equations.

The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.

Dizertační práce se zabývá slabě zpožděnými lineárními rovinnými systémemy s konstantními koeficienty. Charakteristická rovnice těchto systémů je identická s charakteristickou rovnicí systému, který neobsahuje zpožděné členy. V takovém případě se počáteční dimenze prostoru řešení mění po několika krocích na menší. V jistém smyslu je tato situace analogická podobnému jevu v teorii lineárních diferenciálních systémů s konstantními koeficienty a speciálním zpožděním, kdy původně nekonečně rozměrný prostor řešení (na počátečním intervalu) přejde po několika krocích do konečného prostoru řešení. V práci je pro každý možný případ kombinace kořenů charakteristické rovnice konstruováno obecné řešení daného systému a jsou formulovány výsledky o dimenzi prostoru řešení. Také je zkoumána stabilita řešení.

The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um die Stabilität zu garantieren, benutzen wir die Glattheit der Lösung, dann erhalten wir eine sogenannte bedingte Stabilität. Wir demonstrieren die sogenannte Interpolationsmethode zur Herleitung von bedingten Stabilitätsabschätzungen bei inversen Problemen für partielle Differentialgleichungen.

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um die Stabilität zu garantieren, benutzen wir die Glattheit der Lösung, dann erhalten wir eine sogenannte bedingte Stabilität. Wir demonstrieren die sogenannte Interpolationsmethode zur Herleitung von bedingten Stabilitätsabschätzungen bei inversen Problemen für partielle Differentialgleichungen.