Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

Social Inequality and Social Policy outside the OECD

Almost all Latin American countries are still marked by extreme forms of social inequality – and to an extent, this seems to be the case regardless of national differences in the economic development model or the strength of democracy and the welfare state. Recent research highlights the fact that the heterogeneous labour markets in the region are a key source of inequality. At the same time, there is a strengthening of ‘exclusive’ social policy, which is located at the fault lines of the labour market and is constantly (re-)producing market-mediated disparities. In the last three decades, this type of social policy has even enjoyed democratic legitimacy. These dynamics challenge many of the assumptions guiding social policy and democratic theory, which often attempt to account for the specificities of the region by highlighting the purported flaws of certain policies. We suggest taking a different perspective: social policy in Latin American should not be grasped as a deficient or flawed type of social policy, but as a very successful relation of political domination. ‘Relational social analysis’ locates social policy in the ‘tension zone’ constituted by the requirements of economic reproduction, demands for democratic legitimacy and the relative autonomy of the state. From this vantage point, we will make the relation of domination in question accessible for empirical research. It seems particularly useful for this purpose to examine the recent shifts in the Latin American labour markets, which have undergone numerous reforms. We will examine which mechanisms, institutions and constellations of actors block or activate the potentials of redistribution inherent in such processes of political reform. This will enable us to explore the socio-political field of forces that has been perpetuating the social inequalities in Latin America for generations.

Individualisierung und Sozialstruktur - objektive und subjektive Dimensionen sozialer Ungleichheit

Die Dissertation "Individualisierung und Sozialstruktur - objektive und subjektive Dimensionen sozialer Ungleichheit" setzt sich mit einem zentralen Problem der gegenwärtigen Sozialstrukturforschung in den westlichen Industrienationen und im Speziellen in Deutschland auseinander: Im Zuge der Diskussion um die Modernisierung und Individualisierung gesellschaftlicher Strukturen sind die Begriffe "Klasse" und "Schicht" sowie die zugehörigen theoretischen und methodischen Konzepte zunehmender Kritik ausgesetzt. Als ein Resultat dieser Debatte kann die zunehmende Popularität neuer Konzepte angesehen werden, die soziale Differenzierungen eher in einem horizontal-soziokulturellen Kontext deuten und theoretisch an das Individuum knüpfen. Die vorliegende Arbeit zeigt, dass diese "neuen" Milieu- und Lebensstilmodelle einen radikalen Bruch mit den theoretischen Grundlagen der Sozialstrukturanalyse darstellen und als holistische Modelle zur Beschreibung und Deutung sozialer Strukturen ebenso einseitig erscheinen, wie das ihrerseits kritisierte vertikale Paradigma der Klassen- und Schichtungssoziologie. Aus diesem Grunde wird hier ein integratives Konzept entwickelt und vorgeschlagen, das objektive und subjektive Dimensionen sozialer Ungleichheit in einem einheitlichem theoretischen Rahmen sinnvoll miteinander verknüpft und somit in der Lage ist Aspekte von Individualisierung und vertikaler Ungleichheit zu verbinden. Die vielseitigen Möglichkeiten und Vorteile, die ein solches "flexibles Habituskonzept" im Sinne einer umfassenderen und zeitgemäßen Sozialstrukturanalyse bietet, werden anhand einer Sekundäranalyse aktueller Daten aus der Lebensstilforschung aufgezeigt und können somit die entwickelte theoretische Perspektive nachhaltig bestätigen.

Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

Uncover the Concealed Link: Gender & Ethnicity-Divided Local Knowledge on the Agro-Ecosystem of a Forest Margin

This research is a study about knowledge interface that aims to analyse knowledge discontinuities, the dynamic and emergent characters of struggles and interactions within gender system and ethnicity differences. The cacao boom phenomenon in Central Sulawesi is the main context for a changing of social relations of production, especially when the mode of production has shifted or is still underway from subsistence to petty commodity production. This agrarian change is not only about a change of relationship and practice, but, as my previous research has shown, also about the shift of knowledge domination, because knowledge construes social practice in a dialectical process. Agroecological knowledge is accumulated through interaction, practice and experience. At the same time the knowledge gained from new practices and experiences changes mode of interaction, so such processes provide the arena where an interface of knowledge is manifested. In the process of agro-ecological knowledge interface, gender and ethnic group interactions materialise in the decision-making of production and resource allocation at the household and community level. At this point, power/knowledge is interplayed to gain authority in decision-making. When authority dominates, power encounters resistance, whereas the dominant power and its resistance are aimed to ensure socio-economic security. Eventually, the process of struggle can be identified through the pattern of resource utilisation as a realisation of production decision-making. Such processes are varied from one community to another, and therefore, it shows uniqueness and commonalities, especially when it is placed in a context of shifting mode of production. The focus is placed on actors: men and women in their institutional and cultural setting, including the role of development agents. The inquiry is informed by 4 major questions: 1) How do women and men acquire, disseminate, and utilise their agro ecological knowledge, specifically in rice farming as a subsistence commodity, as well as in cacao farming as a petty commodity? How and why do such mechanisms construct different knowledge domains between two genders? How does the knowledge mechanism apply in different ethnics? What are the implications for gender and ethnicity based relation of production? ; 2) Using the concept of valued knowledge in a shifting mode of production context: is there any knowledge that dominates others? How does the process of domination occur and why? Is there any form of struggle, strategies, negotiation, and compromise over this domination? How do these processes take place at a household as well as community level? How does it relate to production decision-making? ; 3) Putting the previous questions in two communities with a different point of arrival on a path of agricultural commercialisation, how do the processes of struggle vary? What are the bases of the commonalities and peculiarities in both communities?; 4) How the decisions of production affect rice field - cacao plantation - forest utilisation in the two villages? How does that triangle of resource use reflect the constellation of local knowledge in those two communities? What is the implication of this knowledge constellation for the cacao-rice-forest agroecosystem in the forest margin area? Employing a qualitative approach as the main method of inquiry, indepth and dialogic interviews, participant observer role, and document review are used to gather information. A small survey and children’s writing competition are supplementary to this data collection method. The later two methods are aimed to give wider information on household decision making and perception toward the forest. It was found that local knowledge, particularly knowledge pertaining to rice-forest-cacao agroecology is divided according to gender and ethnicity. This constellation places a process of decision-making as ‘the arena of interface’ between feminine and masculine knowledge, as well as between dominant and less dominant ethnic groups. Transition from subsistence to a commercial mode of production is a context that frames a process where knowledge about cacao commodity is valued higher than rice. Market mechanism, as an external power, defines valued knowledge. Valued knowledge defines the dominant knowledge holder, and decision. Therefore, cacao cultivation becomes a dominant practice. Its existence sacrifices the presence of rice field and the forest. Knowledge about rice production and forest ecosystem exist, but is less valued. So it is unable to challenge the domination of cacao. Various forms of struggles - within gender an ethnicity context - to resist cacao domination are an expression of unequal knowledge possession. Knowledge inequality implies to unequal access to withdraw benefit from market valued crop. When unequal knowledge fails to construct a negotiated field or struggles fail to reveal ‘marginal’ decision, e.g. intensification instead of cacao expansion to the forest, interface only produces divergence. Gender and ethnicity divided knowledge is unabridged, since negotiation is unable to produce new knowledge that accommodates both interests. Rice is loaded by ecological interest to conserve the forest, while cacao is driven by economic interest to increase welfare status. The implication of this unmediated dominant knowledge of cacao production is the construction of access; access to the forest, mainly to withdraw its economic benefit by eliminating its ecological benefit. Then, access to cacao as the social relationship of production to acquire cacao knowledge; lastly, access to defend sustainable benefit from cacao by expansion. ‘Socio-economic Security’ is defined by Access. The convergence of rice and cacao knowledge, however, should be made possible across gender and ethnicity, not only for the sake of forest conservation as the insurance of ecological security, but also for community’s socio-economic security. The convergence might be found in a range of alternative ways to conduct cacao sustainable production, from agroforestry system to intensification.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Familiale Bewegungssozialisation

Familiale Bewegungssozialisation – Zum Einfluss der Herkunftsfamilie auf die Bewegungssozialisation von Grundschulkindern. Die zentrale Fragestellung der Schrift ist, welchen Einfluss die soziale Herkunft auf die Bewegungssozialisation und Bewegungsentwicklung von Kindern im Grundschulalter hat. Die Auswirkungen sozialer Ungleichheit auf die Bewegungssozialisation, insbesondere die motorische Entwicklung, wurden in der Sportwissenschaft noch unzureichend untersucht. Der Arbeit liegt die Sozialisationstheorie von Witte (1994) zugrunde; mit ihrer Hilfe wird versucht die motorische Entwicklung theoriegeleitet zu erklären. Dafür werden Merkmale der Bewegungssozialisation und der motorischen Entwicklung in das theoretische Rahmenkonzept von Witte (1994) eingesetzt. Zu Beginn (Kapitel 1) erklärt die Arbeit den Begriff der sozialen Herkunft. Es werden der soziale Status, die Familienform und der Migrationshintergrund als Bestandteile der sozialen Herkunft definiert. Im weiteren Verlauf (Kapitel 2) wird die Sozialisationsinstanz Familie und die verschiedenen Familienformen vor dem Hintergrund sozialer Ungleichheit dargelegt. Das dritte Kapitel widmet sich dem sozialisationstheoretischen Konzept. Es werden die Sozialisationstheorie von Hurrelmann, die Körper- und Bewegungskarriere von Baur und das theoretische Rahmenkonzept der Sozialisation von Witte erklärt. Kapitel 4 beschreibt den Forschungsstand und Kapitel 5 stellt die Modellbildung und die Herleitung der Hypothesen dar. Die empirische Untersuchung fand an ausgewählten Grundschulen der Stadt Kassel statt. Insgesamt wurden 251 Kinder im Alter von 7-10 Jahren mit dem AST 6-11 untersucht und deren Eltern mit einem eigens entwickelten Fragebogen befragt. Die Daten wurden mit Hilfe von multivariaten Verfahren in Beziehung zueinander gesetzt. Die Ergebnisse zeigen, dass sich Grundschulkinder hinsichtlich ihrer motorischen Entwicklung nicht in Abhängigkeit der sozialen Herkunft unterscheiden. Jedoch ist das Sportklima der Familien sehr stark abhängig von der sozialen Herkunft. Es wird deutlich, dass Kinder aus sozial benachteiligten Familien, aus Ein-Eltern-Familien und mit Migrationshintergrund schlechtere Möglichkeiten haben sich in ihrer Bewegungssozialisation zu entfalten. Die Prüfung des Sozialisationsmodells zeigt, neben der guten Operationalisierbarkeit des Modells, dass die Modellvariable „Orientierung“ (Orientierung der Familie hinsichtlich der Bedeutung von Bewegung und Sport) den größten Einfluss auf die Bewegungssozialisation von Kindern hat.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

China's Labor Question

The Honda workers’ strike in 2010 attracted world wide attention. It was one of thousands of labor disputes that happen every year in China, but it was the first major calling for the right of workers to represent themselves in collective bargaining. The question of representation is therefore the main topic of the book. The various contributors to this volume share the view that the Chinese party-state takes the protest against social inequality seriously. It has enacted many laws aimed at channeling dissatisfaction into safe channels. The implementation of these laws, however, lags behind and these laws do not include the right of freedom of association. Without this right, super-exploitation will persist and the system of labor relations will remain prone to eruptive forms of protest. The first part of the book provides an overview of the economic context of Chinese labor relations, the transformation of class-relations, the evolution of labor law, and government policies intended to set a wage floor. Based on extensive field research, the second part looks at the evolution of labor relations at the industry level. In the third part, the focus shifts to the Corporate Social Responsibility agenda in China. The final part looks at the connection between land reform and social inequality.

Individual Decision-Making and Inflation Persistence

The traditional task of a central bank is to preserve price stability and, in doing so, not to impair the real economy more than necessary. To meet this challenge, it is of great relevance whether inflation is only driven by inflation expectations and the current output gap or whether it is, in addition, influenced by past inflation. In the former case, as described by the New Keynesian Phillips curve, the central bank can immediately and simultaneously achieve price stability and equilibrium output, the so-called ‘divine coincidence’ (Blanchard and Galí 2007). In the latter case, the achievement of price stability is costly in terms of output and will be pursued over several periods. Similarly, it is important to distinguish this latter case, which describes ‘intrinsic’ inflation persistence, from that of ‘extrinsic’ inflation persistence, where the sluggishness of inflation is not a ‘structural’ feature of the economy but merely ‘inherited’ from the sluggishness of the other driving forces, inflation expectations and output. ‘Extrinsic’ inflation persistence is usually considered to be the less challenging case, as policy-makers are supposed to fight against the persistence in the driving forces, especially to reduce the stickiness of inflation expectations by a credible monetary policy, in order to reestablish the ‘divine coincidence’. The scope of this dissertation is to contribute to the vast literature and ongoing discussion on inflation persistence: Chapter 1 describes the policy consequences of inflation persistence and summarizes the empirical and theoretical literature. Chapter 2 compares two models of staggered price setting, one with a fixed two-period duration and the other with a stochastic duration of prices. I show that in an economy with a timeless optimizing central bank the model with the two-period alternating price-setting (for most parameter values) leads to more persistent inflation than the model with stochastic price duration. This result amends earlier work by Kiley (2002) who found that the model with stochastic price duration generates more persistent inflation in response to an exogenous monetary shock. Chapter 3 extends the two-period alternating price-setting model to the case of 3- and 4-period price durations. This results in a more complex Phillips curve with a negative impact of past inflation on current inflation. As simulations show, this multi-period Phillips curve generates a too low degree of autocorrelation and too early turnings points of inflation and is outperformed by a simple Hybrid Phillips curve. Chapter 4 starts from the critique of Driscoll and Holden (2003) on the relative real-wage model of Fuhrer and Moore (1995). While taking the critique seriously that Fuhrer and Moore’s model will collapse to a much simpler one without intrinsic inflation persistence if one takes their arguments literally, I extend the model by a term for inequality aversion. This model extension is not only in line with experimental evidence but results in a Hybrid Phillips curve with inflation persistence that is observably equivalent to that presented by Fuhrer and Moore (1995). In chapter 5, I present a model that especially allows to study the relationship between fairness attitudes and time preference (impatience). In the model, two individuals take decisions in two subsequent periods. In period 1, both individuals are endowed with resources and are able to donate a share of their resources to the other individual. In period 2, the two individuals might join in a common production after having bargained on the split of its output. The size of the production output depends on the relative share of resources at the end of period 1 as the human capital of the individuals, which is built by means of their resources, cannot fully be substituted one against each other. Therefore, it might be rational for a well-endowed individual in period 1 to act in a seemingly ‘fair’ manner and to donate own resources to its poorer counterpart. This decision also depends on the individuals’ impatience which is induced by the small but positive probability that production is not possible in period 2. As a general result, the individuals in the model economy are more likely to behave in a ‘fair’ manner, i.e., to donate resources to the other individual, the lower their own impatience and the higher the productivity of the other individual. As the (seemingly) ‘fair’ behavior is modelled as an endogenous outcome and as it is related to the aspect of time preference, the presented framework might help to further integrate behavioral economics and macroeconomics.

Small and Closed vs. Large and Open: Some Lessons from Comparing Cuban to Colombian Agricultural Development

Comparing the experiences of selected Latin America and the Caribbean countries and their trajectories over the past 15 years offers rich insights into the dynamics and causes for not meeting the 2015 MDGs. They also offer clues for post-MDG strategies. Central to achieving sustainable growth are government policies able to support small and medium-sized farms and peasants, as they are crucial for the achievement of several goals, centrally: to achieve food security; to provide a sound and stable rural environment able to resist external (financial) shocks; to secure healthy food; to secure local food; and to protect vibrant and culturally rich local communities. This paper analyses and compares the most successful government policies to the least successful policies carried out over the last 15 years in selected Latin American and Caribbean countries and based on this analysis, offers strategies for more promising post-MDG politics, able to reduce poverty, reduce inequality, fight back informality, and achieve more decent work in poor countries.

Demokratie und Dekolonisierung in Bolivien

Ausgehend von den fortdauernden Ausschlüssen und strukturellen Benachteiligungen der indigenen Bevölkerung Lateinamerikas kritisiert die vorliegende Arbeit die begrenzten Möglichkeiten gesellschaftlicher Teilhabe innerhalb von liberalen Wahldemokratien. Neben materiellen Ungleichheiten stehen immaterielle Formen der Ungleichheit, wie kulturelle und symbolische Barrieren politischer sowie sozialer Teilhabe im Fokus der Analyse. Das Forschungs- und Erkenntnisinteresse zielt darauf, Demokratie nicht länger nur anhand liberal-repräsentativer Normen und Verfahren zu erfassen und zu werten. Es geht um die Reflexion anderer demokratischer Praxen, wie indigener und indigen-gewerkschaftlicher Formen lokaler Selbstregierung in Bolivien. Denn im bolivianischen Transformationsprozess mündete die Kritik der liberal-repräsentativen Demokratie in einer doppelten Forderung: Zum einen wird die Demokratisierung der liberalen Demokratie und zum anderen ihre Dekolonisierung gefordert. Die Dekolonisierung und Institutionalisierung unterschiedlicher Praxen und Vorstellungen wird empirisch am Beispiel des indigenen Autonomieprozesses untersucht. Auf nationaler Ebene werden die Demokratisierungsfortschritte u. a. anhand von Wahlrecht, der Entwicklung der Partizipation und Repräsentation bilanziert und die materielle Dimension von Teilhabe auf Grundlage der sozial- und wirtschaftspolitischen Reformen der Regierung Morales geprüft.

Institutions, Behavior and Evolution

The three articles constituting this thesis are for reasons of content or method related to the following three fields in economics: Behavioral Economics, Evolutionary Game Theory and Formal Institutional Economics. A core element of these fields is the concept of individual preferences. Preferences are of central importance for the conceptional framework to analyze human behavior. They form the foundation for the theory of rational choice which is defined by the determination of the choice set and the selection of the most preferred alternative according to some consistency requirements. The theory of rational choice is based on a very simplified description of the problem of choice (object function and constraints). However, that choices depend on many more factors is for instance propagated by psychological theories and is supported by many empirical and experimental studies. This thesis adds to a better understanding of individual behavior to the extent that the evolution of certain characteristics of preferences and their consequences on human behavior forms the overarching theme of the dissertation. The long-term effect of evolutionary forces on a particular characteristic of importance in the theoretical, empirical and experimental economic literature, the concept of inequality aversion, is subject of the article “The evolution of inequality aversion in a simplified game of life” (Chapter 4). The contribution of the article is the overcoming of a restriction of former approaches to analyze the evolution of preferences in very simple environments. By classifying human interaction into three central economic games, the article provides a first step towards a simplified and sufficiently complete description of the interaction environment. Within such an environment the article characterizes the evolutionary stable preference distribution. One result shows, that the interaction of the aforementioned three classes can stabilize a preference of inequality aversion in the subpopulation which is favored in the problem of redistribution. The two remaining articles are concerned with social norms, which dissemination is determined by medium-run forces of cultural evolution. The article “The impact of market innovations on the evolution of social norms: the sustainability case.“ (Chapter 2) studies the interrelation between product innovations which are relevant from a sustainability perspective and an according social norm in consumption. This relation is based on a conformity bias in consumption and the attempt to avoid cognitive dissonances resulting from non-compliant consumption. Among others, it is shown that a conformity bias on the consumption side can lead to multiple equilibria on the side of norm adoption. The article “Evolution of cooperation in social dilemmas: signaling internalized norms.” (Chapter 3) studies the emergence of cooperation in social dilemmas based on the signaling of social norms. The article provides a potential explanation of cooperative behavior, which does not rely on the assumption of structured populations or on the unmotivated ability of social norms to restrict individual actions or strategy spaces. A comprehensive result of the single articles is the explanation of the phenomenon of partial norm adaption or dissemination of preferences. The plurality of the applied approaches with respect to the proximity to the rational choice approach and regarding the underlying evolutionary mechanics is a particular strength of the thesis. It shows the equality of these approaches in their potential to explain the phenomenon of cooperation in environments that provide material incentives for defective behavior. This also points to the need of a unified framework considering the biological and cultural coevolution of preference patterns.