Bøger af Thomas Schuster

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Amphiphilic molecules spontaneously self-assemble into a variety of structures in solution. The term amphiphilic indicates that one part of the molecule is attracted to the solvent, while the other is not. Interactions such as between solute-solvent and solute-solute thus determine the organization. Understanding the self-assembly means understanding those interactions and their driving forces. In the first chapter an overview of the self-organization of amphiphilic molecules into supermolecuar aggregates of different morphologies is provided, with a focus on purely peptidic amphiphiles, i.e. amphiphiles which consist solely of a different amino acid sequence. In the second chapter the self-assembly of amphiphilic peptides with a specific amino acid sequence into micelles and spherical peptide nanoparticles is described. The undecamer peptide that was used features a repetitive L-tryptophan and D-leucine [LW-DL] motif, representing the hydrophobic block ¿ which is a truncated version of gramicidin A (gA), named gT. The N-terminally attached hydrophilic section was either lysine (K) or acetylated lysine (X) and was optionally terminated with cysteine for post-functionalization of the thiol-group. The uncharged peptide AcC-X3-gT was demonstrated to assemble into micelles and subsequently into peptide particles, termed ¿peptide beads¿. We hypothesize that the peptide beads consisted of micelles ¿ a structure described as multicompartment micelles. Peptide beads using AcC-X3-gT and its analogues ¿ including Ac-X3-gT-C, a new peptide with the cysteine residue on the C instead of the N-terminus ¿ are further investigated in Chapter Three. We succeeded in creating highly ordered Ac-X3-gT-C ¿ Au-NP composites, which allowed us to visualize the inner structure of the nanoparticles. The presented composite materials are expected to exhibit exceptional electrical and optical properties.

Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.

Explores why the expansion of economic communication has proven to be of only limited benefit. This book argues that the financial media boom has had negative repercussions resulting in substantial costs for the individual as well as the systemic level.

¿Das Buch vermittelt fundierte Kenntnisse in der Investitionsrechnung von Unternehmen. Sie erlernen die Rahmenbedingungen weiterer Verfahren der Investitionsplanung, insbesondere die Sensitivitäts-, die Break-even-, die Szenarioanalyse sowie die Simulation und beherrschen deren Anwendung. Darüber hinaus können Sie nach Erarbeitung die Modifikation der Investitionsrechnungen bei der Einführung von realitätsnäheren Annahmen, wie z. B. Steuern, nachvollziehen und Sie sind dann auch in der Lage, diese selbstständig anzuwenden. Sie sind darüber hinaus imstande die erlernten Inhalte auf konkrete praxisrelevante Entscheidungssituationen (z. B. verschiedene Investitionsarten) zu übertragen und können diese auch auf weiterführende Problemstellungen (z. B. Unternehmensbewertungen) anwenden.