Mit der Blickrichtung auf die Synthese und Darstellung neuer Verbindungen zur Verbesserung der Lebensqualität, Grundbedürfnisse und Gesundheit einer modernen Gesellschaft sind neue Strategien, welche die Konzepte der Nachhaltigkeit, Effizienz und Umweltschutz verinnerlichen, von immenser Bedeutung. Multikomponentenreaktionen (MCRs) offerieren hierfür einen attraktiven Lösungsansatz. Als Eintopfreaktionen zeichnen sich MCRs durch hohe Stufen- sowie Atomökonomien aus und können ferner dazu beitragen Kosten, Zeit, Energie und Abfälle einzusparen. Durch den modularen Charakter von MCRs lassen sich darüber hinaus schnell und effizient eine Vielzahl unterschiedlicher Molekülstrukturen generieren. Vor diesem Hintergrund konnten im Rahmen dieser Forschungsarbeit einige neue, kombinatorische Konzepte zur Synthese α-substituierter Glycinderivate entwickelt werden. Ausgehend von einer weiterentwickelten, Pd-katalysierten, enantioselektiven 3-Komponentenreaktion auf Basis von Sulfonsäureamiden, Glyoxylsäure Monohydrat und Boronsäuren konnte eine unerwartete Hintergrundreaktion festgestellt werden, die sich schlussendlich als erste katalysatorunabhängige Petasis-Reaktion auf Basis von Sulfonsäureamiden als Amin-Komponente darstellte. In Anbetracht der Aufgabe eine ressourcensparende und nachhaltigere Aufbaumöglichkeit von unnatürlichen Aminosäurederivaten zu entwickeln, gelang es im Zuge dieser Doktorarbeit weiterhin eine Pd-katalysierte, decarboxylative 3-Komponentenreaktion aufzubauen und zu etablieren. Dabei bieten Arylcarbonsäuren als Schlüsselkomponenten in einem decarboxylativen Konzept mit Palladium eine kostengünstigere und umweltfreundlichere Alternative zu den bisher bestehenden Methoden mit Organoboronsäuren oder anderer Organometall-Spezies. Überraschenderweise konnte im Zuge der Untersuchungen zur Substratbreite der Aldehyd-Komponente eine direkte, decarboxylative Addition zwischen den eingesetzten Arylcarbonsäuren und den verschiedenen Glyoxylsäureestern beobachtet werden. Dabei eröffnete diese Methode in ersten Untersuchungen eine interessante Möglichkeit zur Darstellung entsprechender Mandelsäurederivate.

Risk management is an indispensable component of the financial system. In this context, capital requirements are built by financial institutions to avoid future bankruptcy. Their calculation is based on a specific kind of maps, so-called risk measures. There exist several forms and definitions of them. Multi-asset risk measures are the starting point of this dissertation. They determine the capital requirements as the minimal amount of money invested into multiple eligible assets to secure future payoffs. The dissertation consists of three main contributions: First, multi-asset risk measures are used to calculate pricing bounds for European type options. Second, multi-asset risk measures are combined with recently proposed intrinsic risk measures to obtain a new kind of a risk measure which we call a multi-asset intrinsic (MAI) risk measure. Third, the preferences of an agent are included in the calculation of the capital requirements. This leads to another new risk measure which we call a scalarized utility-based multi-asset (SUBMA) risk measure. In the introductory chapter, we recall the definition and properties of multi-asset risk measures. Then, each of the aforementioned contributions covers a separate chapter. In the following, the content of these three chapters is explained in more detail: Risk measures can be used to calculate pricing bounds for financial derivatives. In Chapter 2, we deal with the pricing of European options in an incomplete financial market model. We use the common risk measures Value-at-Risk and Expected Shortfall to define good deals on a financial market with log-normally distributed rates of return. We show that the pricing bounds obtained from Value-at-Risk may have a non-smooth behavior under parameter changes. Additionally, we find situations in which the seller's bound for a call option is smaller than the buyer's bound. We identify the missing convexity of the Value-at-Risk as main reason for this behavior. Due to the strong connection between the obtained pricing bounds and the theory of risk measures, we further obtain new insights in the finiteness and the continuity of multi-asset risk measures. In Chapter 3, we construct the MAI risk measure. Therefore, recall that a multi-asset risk measure describes the minimal external capital that has to be raised into multiple eligible assets to make a future financial position acceptable, i.e., that it passes a capital adequacy test. Recently, the alternative methodology of intrinsic risk measures was introduced in the literature. These ask for the minimal proportion of the financial position that has to be reallocated to pass the capital adequacy test, i.e., only internal capital is used. We combine these two concepts and call this new type of risk measure an MAI risk measure. It allows to secure the financial position by external capital as well as reallocating parts of the portfolio as an internal rebooking. We investigate several properties to demonstrate similarities and differences to the two aforementioned classical types of risk measures. We find out that diversification reduces the capital requirement only in special situations depending on the financial positions. With the help of Sion's minimax theorem we also prove a dual representation for MAI risk measures. Finally, we determine capital requirements in a model motivated by the Solvency II methodology. In the final Chapter 4, we construct the SUBMA risk measure. In doing so, we consider the situation in which a financial institution has to satisfy a capital adequacy test, e.g., by the Basel Accords for banks or by Solvency II for insurers. If the financial situation of this institution is tight, then it can happen that no reallocation of the initial endowment would pass the capital adequacy test. The classical portfolio optimization approach breaks down and a capital increase is needed. We introduce the SUBMA risk measure which optimizes the hedging costs and the expected utility of the institution simultaneously subject to the capital adequacy test. We find out that the SUBMA risk measure is coherent if the utility function has constant relative risk aversion and the capital adequacy test leads to a coherent acceptance set. In a one-period financial market model we present a sufficient condition for the SUBMA risk measure to be finite-valued and continuous. Finally, we calculate the SUBMA risk measure in a continuous-time financial market model for two benchmark capital adequacy tests.

The main objects of study in this thesis are abelian varieties and their endomorphism rings. Abelian varieties are not just interesting in their own right, they also have numerous applications in various areas such as in algebraic geometry, number theory and information security. In fact, they make up one of the best choices in public key cryptography and more recently in post-quantum cryptography. Endomorphism rings are objects attached to abelian varieties. Their computation plays an important role in explicit class field theory and in the security of some post-quantum cryptosystems. There are subexponential algorithms to compute the endomorphism rings of abelian varieties of dimension one and two. Prior to this work, all these subexponential algorithms came with a probability of failure and additional steps were required to unconditionally prove the output. In addition, these methods do not cover all abelian varieties of dimension two. The objective of this thesis is to analyse the subexponential methods and develop ways to deal with the exceptional cases. We improve the existing methods by developing algorithms that always output the correct endomorphism ring. In addition to that, we develop a novel approach to compute endomorphism rings of some abelian varieties that could not be handled before. We also prove that the subexponential approaches are simply not good enough to cover all the cases. We use some of our results to construct a family of abelian surfaces with which we build post-quantum cryptosystems that are believed to resist subexponential quantum attacks - a desirable property for cryptosystems. This has the potential of providing an efficient non interactive isogeny based key exchange protocol, which is also capable of resisting subexponential quantum attacks and will be the first of its kind.

Membrane proteins are of high pharmacological interest as they are involved in a variety of vital functions. However, to make them accessible to in vitro studies, they often need to be extracted from their natural lipid environment and stabilized with the aid of membrane-mimetic systems. Such membrane mimics can consist of diverse amphiphilic molecules. Small-molecule amphiphiles that can solubilize lipid bilayers, so-called detergents, have been invaluable tools for membrane-protein research in recent decades. Herein, novel small-molecule glyco-amphiphiles embodying three distinct design principles are introduced, and their biophysical and physicochemical properties are investigated. In doing so, the major aims consist in establishing new promising amphiphiles and in determining structure–efficacy relationships for their synthesis and application. First, the software package D/STAIN was introduced to facilitate the analysis of demicellization curves obtained by isothermal titration calorimetry. The robustness of the underlying algorithm was demonstrated by analyzing demicellization curves representing large variations in amphiphile concentrations and thermodynamic parameters. Second, the interactions of diastereomeric cyclopentane maltoside amphiphiles (CPMs) with lipid bilayers and membrane proteins were investigated. To this end, lipid model membranes, cellular membranes, and model membrane proteins were treated with different stereoisomer CPMs. These investigations pointed out the importance of stereochemical configuration in the solubilization of lipid bilayers, in the extraction of membrane proteins, and, ultimately, in the stabilization of the latter. Ultimately, CPM C12 could be identified as a particularly stabilizing agent. Third, the influence of a polymerizable group attached to detergent-like amphiphiles was characterized regarding their micellization, micellar properties, and ability to solubilize lipid membranes. This revealed that such chemical modifications can have different degrees of impact regarding the investigated properties. In particular, micellization was influenced substantially, whereas the sizes of the resulting micelles varied slightly. The polymerizable amphiphiles were shown to solubilize artificial and natural lipid membranes and, consequently, to extract membrane proteins. Last, the self-assembly of diglucoside amphiphiles bearing either a hydrocarbon or a lipophobic fluorocarbon chain to form native nanodiscs was investigated. It was shown that the presence of a fluorocarbon hydrophobic chain conveys superior stabilization properties onto the amphiphile and the resulting nanodiscs. Moreover, the kinetics of lipid exchange were fundamentally altered by the presence of the fluorocarbon amphiphiles in the nanodisc rim.

Die Anbieter von Produkt-Service Systemen (PSS) im Investitionsgüterbereich unterliegen zunehmend dem Einfluss einer VUKA-Welt. Neue Technologien und Geschäftsmodelle, sich schnell ändernde Kundenbedürfnisse und der Einbezug vieler interner und externer Akteure resultieren in Komplexität, Unsicherheiten und kurzfristigen Änderungen, auf welche die PSS-Anbieter reagieren müssen, um frühzeitig entsprechende Lösungen anbieten zu können. Die PSS-Planung befasst sich mit der Identifikation und Spezifikation neuer PSS-Ideen. Die meisten Vorgehen zur PSS-Planung fokussieren auf die Planung von Sachprodukten, Serviceprodukten, unterstützender Infrastruktur und Netzwerke von Akteuren und binden den Kunden in die Planung ein. Durch die genannten Einflüsse der VUKA-Welt auf die Planung von PSS, muss diese an sich schnell ändernde Gegebenheiten angepasst werden. Agile Methoden der Softwareentwicklung bieten hierfür Potenziale. Insbesondere die Agile Methode Design Thinking, die den Kunden innerhalb eines kurzzyklischen Vorgehens in den Mittelpunkt der Entwicklungstätigkeiten stellt und auf die Entwicklung von Prototypen zur schnellen Realisierung von Lösungen setzt, bietet sich für den Einsatz in der PSS-Planung an. Die Arbeit befasst sich mit der Frage, wie Design Thinking in die PSS-Planung integriert werden kann, um zukünftig auf Änderungen adäquat reagieren zu können und gleichzeitig die Vorteile bestehender Ansätze, wie z. B. Kundenorientierung, nicht zu vernachlässigen. Dabei wird mit Hilfe eines Modellierungsansatzes eine Methode entwickelt, welches mit Rollen, Aktivitäten, Techniken und Ergebnissen den Einsatz von Design Thinking für die agile Planung von PSS ermöglicht, den Kunden an unterschiedlichen Stellen mit einbindet und Rücksprünge bei Änderungen erlaubt. Hervorzuheben ist, dass die Methode sowohl technologiegetrieben als auch marktgetrieben initiiert werden kann. Validiert wurde die Methode innerhalb eines Verbundprojekts bei der GRIMME Landmaschinenfabrik GmbH & Co. KG.