Bounds on the non-real spectrum of differential operators with indefinite weights

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm-Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.Comment: 27 page

Animation in relational information visualization

In order to be able to navigate in the world without memorizing each detail, the human brain builds a mental map of its environment. The mental map is a distorted and abstracted representation of the real environment. Unimportant areas tend to be collapsed to a single entity while important landmarks are overemphasized. When working with visualizations of data we build a mental map of the data which is closely linked to the particular visualization. If the visualization changes significantly due to changes in the data or the way it is presented we loose the mental map and have to rebuild it from scratch. The purpose of the research underlying this thesis was to investigate and devise methods to create smooth transformations between visualizations of relational data which help users in maintaining or quickly updating their mental map

On largest volume simplices and sub-determinants

We show that the problem of finding the simplex of largest volume in the convex hull of $n$ points in $\mathbb{Q}^d$ can be approximated with a factor of $O(\log d)^{d/2}$ in polynomial time. This improves upon the previously best known approximation guarantee of $d^{(d-1)/2}$ by Khachiyan. On the other hand, we show that there exists a constant $c>1$ such that this problem cannot be approximated with a factor of $c^d$, unless $P=NP$. % This improves over the $1.09$ inapproximability that was previously known. Our hardness result holds even if $n = O(d)$, in which case there exists a \bar c\,^{d}-approximation algorithm that relies on recent sampling techniques, where $\bar c$ is again a constant. We show that similar results hold for the problem of finding the largest absolute value of a subdeterminant of a $d\times n$ matrix

Not every pseudoword disrupts word recognition: an ERP study

BACKGROUND: If all available acoustic phonetic information of words is used during lexical access and consequently stored in the mental lexicon, then all pseudowords that deviate in a single acoustic feature from a word should hamper word recognition. By contrast, models assuming underspecification of redundant phonological information in the mental lexicon predict a differential disruption of word recognition dependent on the phonological structure of the pseudoword. Using neurophysiological measures, the present study tested the predicted asymmetric disruption by assuming that coronal place of articulation for consonants is redundant. METHODS: Event-related potentials (ERPs) were recorded during a lexical decision task. The focus of interest was on word medial consonants. The crucial pseudowords were created by replacing the place of articulation of the medial consonant in German disyllabic words. We analyzed the differential temporal characteristics of the N400 pseudoword effect. RESULTS: N400 amplitudes for pseudowords were enhanced compared to words. As the uniqueness and deviation points differ for coronal and non-coronal items, the ERPs had to be correspondingly adjusted. The adjusted ERPs revealed that the N400 pseudoword effect starts earlier for coronal than for non-coronal pseudoword variants. Thus, non-coronal variants are accepted as words longer than the coronal variants. CONCLUSION: Our results indicate that lexical representations of words containing medial coronal consonants are initially activated by their corresponding non-coronal pseudowords. The most plausible explanation for the asymmetric neuronal processing of coronal and non-coronal pseudoword variants is an underspecified coronal place of articulation in the mental lexicon

Novel Anionic Glycopolymers: Synthesis and Characterization of Poly(Vinyl Saccharide)s based on Methacrylamido- and Maleicamido Saccharides

Polyvinylsaccharide gehören zu der Gruppe wasserlöslicher Glykopolymere. Ihre Struktur besteht aus einer Kohlenstoff-Hauptkette, an der kovalent Saccharidseitengruppen gebunden sind. Das größte Anwendungspotential dieser Polymere lässt sich den Bereichen Medizin, Biochemie und Chemie zuordnen. Die Synthese und Charakterisierung neuer anionischer Polyvinylsaccharide auf der Basis der Disaccharide D-Maltose und D-Lactose wird beschrieben. Die Polyelektrolyte lassen sich hinsichtlich ihrer Synthese und Struktur in zwei Gruppen einteilen. Die erste Gruppe wurde durch Homopolymerisation neutraler Methacrylamidosaccharide hergestellt und anschließend mittels Carboxymethylierung und Sulfatierung polymeranalog zu anionischen Polymeren modifiziert. Im zweiten Fall wurden anionische Maleinsäureamidosaccharide mit den Vinylamiden N-Methylvinylacetamid, N-Vinylacetamid, N-Vinylpyrrolidon und N-Vinylformamid zu hochmolekularen Verbindungen copolymerisiert. Anhand von Untersuchungen der Copolymerisationskinetik ließ sich zeigen, dass die Maleinsäureamidosaccharide in den Copolymeren mit kurzen Vinylamid-Domänen alternieren. Die anionischen Polyvinylsaccharide wurden anhand von Viskosimetrie- und Lichtstreumessungen auf ihre hydrodynamischen Eigenschaften hin untersucht. Die Herstellung dafür erforderlicher Polymerreihen mit variierender Kettenlänge erfolgte durch Ultraschalldegradation.Poly(vinyl saccharide)s belong to the group of water-soluble glycopolymers. Their structure consists of a carbon backbone chain with carbohydrate side groups. The largest application potential of these polymers can be assigned to medicine, biochemistry and chemistry. The synthesis and characterization of new anionic poly(vinyl saccharide)s on the basis of the disaccharides D-maltose and D-lactose are described. These polyelectrolytes can be divided into two groups related to their synthesis and structure. The first group was synthesized by hompolymerization of neutral methacrylamido saccharides and afterwards modified by carboxymethylation and sulfatation to achieve anionic polymers. In the second case anionic maleicamido saccharides were copolymerized with N-methylvinylacetamide, N-vinylacetamide, N-vinylpyrrolidone and N-vinylformamide as comonomers and polymers with high average molecular weight were yielded. Kinetically investigations showed that the maleicamido saccharides in the copolymers alternate with short vinylamide domains. The hydrodynamic properties of the anionic poly(vinyl saccharide)s were characterized by viscosimetry and light scattering. For this purpose ultrasonic degradation were used to form series of polymers with varying chain length

Novel Anionic Glycopolymers: Synthesis and Characterization of Poly(Vinyl Saccharide)s based on Methacrylamido- and Maleicamido Saccharides

Polyvinylsaccharide gehören zu der Gruppe wasserlöslicher Glykopolymere. Ihre Struktur besteht aus einer Kohlenstoff-Hauptkette, an der kovalent Saccharidseitengruppen gebunden sind. Das größte Anwendungspotential dieser Polymere lässt sich den Bereichen Medizin, Biochemie und Chemie zuordnen. Die Synthese und Charakterisierung neuer anionischer Polyvinylsaccharide auf der Basis der Disaccharide D-Maltose und D-Lactose wird beschrieben. Die Polyelektrolyte lassen sich hinsichtlich ihrer Synthese und Struktur in zwei Gruppen einteilen. Die erste Gruppe wurde durch Homopolymerisation neutraler Methacrylamidosaccharide hergestellt und anschließend mittels Carboxymethylierung und Sulfatierung polymeranalog zu anionischen Polymeren modifiziert. Im zweiten Fall wurden anionische Maleinsäureamidosaccharide mit den Vinylamiden N-Methylvinylacetamid, N-Vinylacetamid, N-Vinylpyrrolidon und N-Vinylformamid zu hochmolekularen Verbindungen copolymerisiert. Anhand von Untersuchungen der Copolymerisationskinetik ließ sich zeigen, dass die Maleinsäureamidosaccharide in den Copolymeren mit kurzen Vinylamid-Domänen alternieren. Die anionischen Polyvinylsaccharide wurden anhand von Viskosimetrie- und Lichtstreumessungen auf ihre hydrodynamischen Eigenschaften hin untersucht. Die Herstellung dafür erforderlicher Polymerreihen mit variierender Kettenlänge erfolgte durch Ultraschalldegradation.Poly(vinyl saccharide)s belong to the group of water-soluble glycopolymers. Their structure consists of a carbon backbone chain with carbohydrate side groups. The largest application potential of these polymers can be assigned to medicine, biochemistry and chemistry. The synthesis and characterization of new anionic poly(vinyl saccharide)s on the basis of the disaccharides D-maltose and D-lactose are described. These polyelectrolytes can be divided into two groups related to their synthesis and structure. The first group was synthesized by hompolymerization of neutral methacrylamido saccharides and afterwards modified by carboxymethylation and sulfatation to achieve anionic polymers. In the second case anionic maleicamido saccharides were copolymerized with N-methylvinylacetamide, N-vinylacetamide, N-vinylpyrrolidone and N-vinylformamide as comonomers and polymers with high average molecular weight were yielded. Kinetically investigations showed that the maleicamido saccharides in the copolymers alternate with short vinylamide domains. The hydrodynamic properties of the anionic poly(vinyl saccharide)s were characterized by viscosimetry and light scattering. For this purpose ultrasonic degradation were used to form series of polymers with varying chain length