Some results on the invertibility of Toeplitz plus Hankel operators

The paper deals with the invertibility of Toeplitz plus Hankel operators T(a)+H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t)=b(t)b(1/t). Special attention is paid to the case of piecewise continuous generating functions. In some cases the dimensions of null spaces of the operator $T(a)+H(b)$ and its adjoint are described

Bubbles and incentives: A post-mortem of the Neuer Markt in Germany

This paper aims to shed light on some of the major allocative consequences of financial market bubbles. In March 1997, the Neuer Markt in Germany opened. Six years later, in June 2003, it closed forever. In the interim period lay the spectacular rise and fall of the first and most important European market for hi-tech stocks. Given investors' frenzy, the Neuer Markt was a special kind of natural experiment. For some time, financing constraints were virtually non-existent. Our model of corporate financing shows that bubbles on financial markets will induce entrepreneurs and providers of external finance to enter the 'wrong' contract. Incentive compatibility constraints designed to guarantee that corporate decision-makers behave constructively turn out to be invalid, and managers will know this before shareholders do. Thus, faulty valuation by stock markets may directly induce destructive corporate behaviour: slack, empire building, excessive risk-taking, and fraud. At the time of the IPO, a huge amount of liquidity is injected into the companies, and a dynamic analysis of the balance sheet ratios and income statement items in the following years can teach us the ways in which this liquidity is diffused. We analyse the corresponding dynamics of total assets, tangible assets and equity, as well as the evolution of sales and profits for 204 German non-financial companies out of a total of 326 companies that had their IPO at the Neuer Markt. On the basis of consecutive annual accounts, we retrace the events using a dynamic flow of funds analysis. We assess the explanatory power of our model using non-parametric methods [Median tests, Wilcoxon-Mann-Whitney tests, Kolmogorov-Smirnov tests] and quantile regressions. Our results indicate that valuation has strong and systematic effects on incentives. Experience, as proxied by age at IPO, is shown to have a beneficial effect, whereas support by VC and PE firms does not seem to matter for the success of the enterprises considered. --Bubbles,corporate governance,quantile regressions,nonparametric statistics

Kinetic and Thermodynamic Characterization of the Bacterial Lectin FimH

One fundamental aim of drug discovery is the development of new molecular entities that have a considerably advantage over already existing therapies. Urinary tract infections (UTIs) urgently require an alternative to the conventional antibiotic therapy as resistance rates for antibiotics are increasing. The development of an anti-adhesive UTI treatment strategy with the bacterial lectin FimH as target is a promising approach to remedy such alarming tendencies. FimH is presented by uropathogenic E. coli (UPEC) strains on the tip of type 1 pili and mediates adhesion to mannosylated residues on the urothelium. This interaction prevents the clearance of UPECs during micturition and enables internalization of the pathogens by urothelial cells. Mannoside-derived FimH antagonists are under development and are considered as promising treatment option for UTIs. In contrast to antibiotics, FimH antagonists do not necessarily exert resistance mechanisms against drugs because they block the adhesion of bacteria to the urothelium without killing them or inhibiting their growth. ________ In the present thesis, FimH and its interaction with mannose-based antagonists were biophysically characterized. Additionally, new methodical approaches are introduced, which are relevant not only for a strategic development of FimH antagonists but also for drugs of other therapeutic areas. The following aspects were investigated: ________ Publication 2: The publication “KinITC – One method supports both thermo-dynamic and kinetic SARs” (Chemistry, 2018,24(49), 13049-13057) comments on kinITC-ETC, a new method based on ITC data to reveal the kinetic fingerprint of a drug–target interaction. In this study, kinITC-ETC was independently validated for the first time. Moreover, structural properties of FimH antagonists could be correlated with kinetic parameters of FimH–antagonist interactions. ________ Manuscript 1: The development of an off-rate screening approach is presented in the study “Off-rate screening by surface plasmon resonance – The search for promising lead structures targeting low-affinity FimH”. The method is subsequently applied to screen a mannose-based compound library against full-length FimH. The assay allows classification of structurally diverse FimH antagonist in order to spot chemical classes exhibiting long dissociative half-lives. ________ Publication 3: The lectin domain is conformationally rigid and needs the pilin domain for allosteric propagation. However, the crosstalk between allosteric sites within the lectin domain takes also place in the absence of the pilin domain as demonstrated in the publication “Conformational switch of the bacterial adhesin FimH in the absence of the regulatory domain – Engineering a minimalistic allosteric system” (J. Biol. Chem., 2018, 293(5), 1835-1849). Mutants of the isolated lectin domain, FimHLD R60P and V27C/L34C, exhibited a low-affinity state and mimic full-length FimH regarding its conformational transition upon mannoside binding. ________ Publication 4: The publication “Target-directed dynamic combinatorial chemistry: A study on potentials and pitfalls as exemplified on a bacterial target” (Chemistry, 2017, 23, 11570-11577) illustrates a target-directed dynamic combinatorial chemistry (tdDCC) approach employing reversible acylhydrazone formation with FimH full-length as target. Optimal sample preparation and data procession are discussed in detail. Finally, the results of the tdDCC assay were subsequently compared with the affinity of library constituents by SPR. ________ Publication 5: In the publication “Comparison of affinity ranking by target-directed dynamic combinatorial chemistry and surface plasmon resonance” larger FimH antagonist libraries were screened using the tdDCC method established in publication 3. The comparison of amplification rates of library substituents with respective binding affinities determined by SPR revealed a linear association. Furthermore, the hazardous acylhydrazone moiety could be replaced by various bioisosteres without changing the affinity of the parent compound. ________ Manuscript 2: The hydrogen bond network formed between mannose derivates and the CRD of FimH is extensively elucidated in the manuscript ”High-affinity carbohydrate–lectin interaction: How nature makes it possible”. Computational methods and structural prediction in combination with binding data revealed that the hydrogen bond network forms a unified whole. The removal of only a single hydroxyl group leads to a disruption of the cooperative interplay within the network and consequently results in a dramatic loss in binding affinity. ________ Manuscript 3: In the study “The tyrosine gate of the bacterial adhesion FimH – An evolutionary remnant paves the way for drug discovery”, ITC measurements demonstrated the influence of the tyrosine gate on binding affinity between FimH and natural ligands. While the tyrosine gate is exploited to form optimal hydrophobic interactions with aryl aglycones of synthetic FimH antagonists in order to increase their binding affinity, the tyrosine gate has only a marginal impact on the KD of natural ligands. In contrast to wild-type FimH, mutants that partially or completely lack the tyrosine gate exhibited a comparable binding affinity to dimannoside. ________ Publication 6: The publication “Improvement of aglycone π-stacking yields nanomolar to sub-nanomolar FimH antagonists” displays that fluorination of biphenyl mannosides further improved π-π stacking with the tyrosine gate, reaching nanomolar affinities with FimHFL and even picomolar affinities with FimHLD. It also could be shown that ligand binding to FimHFL occurs with a highly favorable enthalpic and a considerably unfavorable entropic contribution. ________ Publication 7: In the publication “Enhancing the enthalpic contribution of hydrogen bonds by solvent shielding” microcalorimetric studies of FimH could reveal that conformational adaptions of the binding site can establish a solvent-free cavity. Shielding the solvent results in a lower dielectric environment, in which the formation of hydrogen bonds has a considerable enthalpic contribution to the binding free energy. In the case of FimH approximately -13 kJ mol-1 for mannoside binding