Assessment of the GW Approximation using Hubbard Chains

We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable

SUBSPACE CONCENTRATION OF DUAL CURVATURE MEASURES OF SYMMETRIC CONVEX BODIES

We prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body. © 2018 International Press of Boston, Inc. All Rights Reserved

Spectra and total energies from self-consistent many-body perturbation theory

With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GW Gamma scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T matrix. The self-consistent Green's function G, as derived from Dyson's equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results, therefore, suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous. [S0163-1829 (98)05040-1]

Density functional theories and self-energy approaches

A purpose-designed microarray platform (Stressgenes, Phase 1) was utilised to investigate the changes in gene expression within the liver of rainbow trout during exposure to a prolonged period of confinement. Tissue and blood samples were collected from trout at intervals up to 648 h after transfer to a standardised confinement stressor, together with matched samples from undisturbed control fish. Plasma ACTH, cortisol, glucose and lactate were analysed to confirm that the neuroendocrine response to confinement was consistent with previous findings and to provide a phenotypic context to assist interpretation of gene expression data. Liver samples for suppression subtractive hybridisation (SSH) library construction were selected from within the experimental groups comprising “early” stress (2–48 h) and “late” stress (96–504 h). In order to reduce redundancy within the four SSH libraries and yield a higher number of unique clones an additional subtraction was carried out. After printing of the arrays a series of 55 hybridisations were executed to cover 6 time points. At 2 h, 6 h, 24 h, 168 h and 504 h 5 individual confined fish and 5 individual control fish were used with control fish only at 0 h. A preliminary list of 314 clones considered differentially regulated over the complete time course was generated by a combination of data analysis approaches and the most significant gene expression changes were found to occur during the 24 h to 168 h time period with a general approach to control levels by 504 h. Few changes in expression were apparent over the first 6 h. The list of genes whose expression was significantly altered comprised predominantly genes belonging to the biological process category (response to stimulus) and one cellular component category (extracellular region) and were dominated by so-called acute phase proteins. Analysis of the gene expression profile in liver tissue during confinement revealed a number of significant clusters. The major patterns comprised genes that were up-regulated at 24 h and beyond, the primary examples being haptoglobin, β-fibrinogen and EST10729. Two representative genes from each of the six k-means clusters were validated by qPCR. Correlations between microarray and qPCR expression patterns were significant for most of the genes tested. qPCR analysis revealed that haptoglobin expression was up-regulated approximately 8-fold at 24 h and over 13-fold by 168 h.This project was part funded by the European Commission (Q5RS-2001-02211), Enterprise Ireland and the Natural Environment Research Council of the United Kingdom

Unterraumkonzentration von geometrischen Maßen

In this work we study geometric measures in two different extensions of the Brunn-Minkowski theory. The first part of this thesis is concerned with problems in Lp Brunn-Minkowski theory, that is based on the concept of p-addition of convex bodies, which was first introduced by Firey for p = 1 and later considered for all real p by Lutwak et al. The interplay of the volume and other functionals with the p-addition is of particular interest. Considerable open problems in this setting include the validity of extensions of the celebrated Brunn-Minkowski inequality and Minkowski’s inequality, particularly for 0 = p < 1 as the inequalities become stronger for smaller p. The generalization of Minkowski’s inequality to p = 0 is called logarithmic Minkowski inequality, which we will prove here for some particular polytopal instances. The study of the cone-volume measure of convex bodies is another central subject in Lp Brunn-Minkowski theory, which exhibits a strong connection to the logarithmic Minkowski inequality. Fundamental questions in this context ask for a characterization of these measures and when a convex body is uniquely determined by its cone-volume measure. The latter is unknown even for symmetric convex bodies whereas the former problem was solved in this case. The key property in the solution is a concentration bound of a given cone-volume measure restricted to linear subspaces. We will establish a characterization of cone-volume measures of trapezoids and present new examples of convex bodies with non-unique cone-volume measure. Thereby we will discuss how the presence of a subspace concentration bound affects the aforementioned questions. In the second part we consider an only recently discovered family of geometric measures arising in dual Brunn-Minkowski theory. The so-called dual curvature measures of convex bodies act as counterparts of curvature measures in the classical Brunn-Minkowski theory and include the cone-volume measure as a special case. Dual curvature measures gained much interest in the last few years. The task of extending the results obtained for cone-volume measures to the more general dual curvature measures requires novel subspace concentration inequalities. Following the ideas of Kneser and Süss we establish variants of the Brunn-Minkowski inequality under some symmetry assumptions with the aid of which we prove sharp subspace concentration bounds on nearly all dual curvature measures of symmetric convex bodies.In dieser Arbeit untersuchen wir geometrische Maße in zwei verschiedenen Erweiterungen der Brunn-Minkowski-Theorie. Der erste Teil dieser Arbeit befasst sich mit Problemen in der Lp-Brunn-Minkowski-Theorie, die auf dem Konzept der p-Addition konvexer Körper basiert, die zunächst von Firey für p = 1 eingeführt und später von Lutwak et al. für alle reellen p betrachtet wurde. Von besonderem Interesse ist das Zusammenspiel des Volumens und anderer Funktionale mit der p-Addition. Bedeutsame offene Probleme in diesem Setting sind die Gültigkeit von Verallgemeinerungen der berühmten Brunn-Minkowski-Ungleichung und der Minkowski-Ungleichung, insbesondere für 0 = p < 1, da die Ungleichungen für kleinere p stärker werden. Die Verallgemeinerung der Minkowski-Ungleichung auf p = 0 wird als logarithmische Minkowski-Ungleichung bezeichnet, die wir hier für vereinzelte polytopale Fälle beweisen werden. Das Studium des Kegelvolumenmaßes konvexer Körper ist ein weiteres zentrales Thema in der Lp -Brunn-Minkowski-Theorie, das eine starke Verbindung zur logarithmischen Minkowski-Ungleichung aufweist. In diesem Zusammenhang stellen sich die grundlegenden Fragen nach einer Charakterisierung dieser Maße und wann ein konvexer Körper durch sein Kegelvolumenmaß eindeutig bestimmt ist. Letzteres ist für symmetrische konvexe Körper unbekannt, während das erstere Problem in diesem Fall gelöst wurde. Die Schlüsseleigenschaft in der Lösung ist eine Konzentrationsgrenze eines gegebenen Kegelvolumenmaßes eingeschränkt auf lineare Unterräume. Wir werden eine Charakterisierung von Kegelvolumenmaßen von Trapezen herleiten und neue Beispiele konvexer Körper mit nicht-eindeutigem Kegelvolumenmaß präsentieren. Dabei werden wir diskutieren, wie das Vorhandensein einer Schranke an die Konzentration auf Unterräumen die oben genannten Fragen beeinflusst. Im zweiten Teil betrachten wir eine erst kürzlich entdeckte Familie geometrischer Maße, die in der dualen Brunn-Minkowski-Theorie vorkommt. Die sogenannten dualen Krümmungsmaße von konvexen Körpern fungieren als Gegenstücke zu Krümmungsmaßen in der klassischen Brunn-Minkowski-Theorie und schließen das Kegelvolumenmaß als Sonderfall ein. Duale Krümmungsmaße haben in den letzten Jahren großes Interesse geweckt. Die Aufgabe, die Resultate, die für Kegelvolumenmaße erzielt wurden, auf die allgemeineren dualen Krümmungsmaße auszudehnen, erfordert neuartige Abschätzungen der Unterraumkonzentration. Den Ideen von Kneser und Süss folgend, beweisen wir Varianten der Brunn-Minkowski-Ungleichung unter gewissen Symmetrievoraussetzungen, mit deren Hilfe wir scharfe Schranken an die Unterraumkonzentration für nahezu alle dualen Krümmungsmaße symmetrischer konvexer Körper folgern

[Stammbuch Bertha Luise Pollehn]

[STAMMBUCH BERTHA LUISE POLLEHN] [Stammbuch Bertha Luise Pollehn] ( - ) Einband ( - ) Besitzvermerk ( - ) Einträge Bl. 1 - 10 (0v 1r) Einträge Bl. 11 - 20 (10v 11r) Einträge Bl. 21 - 30 (20v 21r) Wachsmalerei ( -