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.

Alternative plant protein sources for pigs and chickens in the tropics – nutritional value and constraints: a review

In the tropics, a large number of smallholder farms contribute significantly to food security by raising pigs and poultry for domestic consumption and for sale on local markets. The high cost and, sometimes, the lack of availability of commercial protein supplements is one of the main limitations to efficient animal production by smallholders. Locally-grown forages and grain legumes offer ecological benefits such as nitrogen fixation, soil improvement, and erosion control which contribute to improve cropping efficiency. Besides these agronomical assets, they can be used as animal feeds in mixed farming systems. In this paper we review options to include locally-grown forages and grain legumes as alternative protein sources in the diets of pigs and poultry in order to reduce farmers’ dependence on externally-purchased protein concentrates. The potential nutritive value of a wide range of forages and grain legumes is presented and discussed. The influence of dietary fibre and plant secondary metabolites contents and their antinutritive consequences on feed intake, digestive processes and animal performances are considered according to the varying composition in those compounds of the different plant species and cultivars covered in this review. Finally, methods to overcome the antinutritive attributes of the plant secondary metabolites using heat, chemical or biological treatment are reviewed regarding their efficiency and their suitability in low input farming systems.

Opportunities and constraints of peri-urban buffalo and dairy cattle systems in Faisalabad, Punjab, Pakistan

In the big cities of Pakistan, peri-urban dairy production plays an important role for household income generation and the supply of milk and meat to the urban population. On the other hand, milk production in general, and peri-urban dairy production in particular, faces numerous problems that have been well known for decades. Peri-urban dairy producers have been especially neglected by politicians as well as non-government-organizations (NGOs). Against this background, a study in Pakistan’s third largest city, Faisalabad (Punjab Province), was carried out with the aims of gathering basic information, determining major constraints and identifying options for improvements of the peri-urban milk production systems. For data collection, 145 peri-urban households (HH) engaged in dairy production were interviewed face to face using a structured and pretested questionnaire with an interpreter. For analyses, HH were classified into three wealth groups according to their own perception. Thus, 38 HH were poor, 95 HH well off and 12 HH rich (26.2%, 65.5% and 8.3%, respectively). The richer the respondents perceived their HH, the more frequently they were actually in possession of high value HH assets like phones, bank accounts, motorbikes, tractors and cars. Although there was no difference between the wealth groups with respect to the number of HH members (about 10, range: 1 to 23), the educational level of the HH heads differed significantly: on average, heads of poor HH had followed education for 3 years, compared to 6 years for well off HH and 8 years for rich HH. About 40% of the poor and well off HH also had off-farm incomes, while the percentage was much higher - two thirds (67%) - for the rich HH. The majority of the HH were landless (62%); the rest (55 HH) possessed agricultural land from 0.1 to 10.1 ha (average 2.8 ha), where they were growing green fodder: maize, sorghum and pearl millet in summer; berseem, sugar cane and wheat were grown in winter. Dairy animals accounted for about 60% of the herds; the number of dairy animals per HH ranged from 2 to 50 buffaloes (Nili-Ravi breed) and from 0 to 20 cows (mostly crossbred, also Sahiwal). About 37% (n=54) of the HH did not keep cattle. About three quarters of the dairy animals were lactating. The majority of the people taking care of the animals were family workers; 17.3% were hired labourers (exclusively male), employed by 11 rich and 32 well off HH; none of the poor HH employed workers, but the percentages were 33.7% for the well off and 91.7% for the rich HH. The total number of workers increased significantly with increasing wealth (poor: 2.0; well off:2.5; rich: 3.4). Overall, 69 female labourers were recorded, making up 16.8% of employed workers and one fourth of the HH’s own labourers. Apparently, their only duty was to clean the animals´ living areas; only one of them was also watering and showering the animals. Poor HH relied more on female workers than the other two groups: 27.1% of the workers of poor HH were women, but only 14.8% and 6.8% of the labour force of well off and rich HH were female. Two thirds (70%) of the HH sold milk to dhodis (middlemen) and one third (35%) to neighbours; three HH (2%) did doorstep delivery and one HH (1%) had its own shop. The 91 HH keeping both species usually sold mixed milk (97%). Clients for mixed and pure buffalo milk were dhodis (78%, respectively 59%) and neighbours (28%, respectively 47%). The highest milk prices per liter (Pakistani Rupees, 100 PKR @ 0.8 Euro) were paid by alternative clients (44 PKR; 4 HH), followed by neighbours (40 PKR, 50 HH); dhodis paid lower prices (36 PKR, 99 HH). Prices for pure buffalo and mixed milk did not differ significantly. However, HH obtaining the maximum price from the respective clients for the respective type of milk got between 20% (mixed milk, alternative clients) and 68% (mixed milk, dhodi) more than HH fetching the minimum price. Some HH (19%) reported 7% higher prices for the current summer than the preceding winter. Amount of milk sold and distance from the HH to the city center did not influence milk prices. Respondents usually named problems that directly affected their income and that were directly and constantly visible to them, such as high costs, little space and fodder shortages. Other constraints that are only influencing their income indirectly, e.g. the relatively low genetic potential of their animals due to neglected breeding as well as the short- and long-term health problems correlated with imbalanced feeding and insufficient health care, were rarely named. The same accounts for problems accompanying improper dung management (storage, disposal, burning instead of recycling) for the environment and human health. Most of the named problems are linked to each other and should be addressed within the context of the entire system. Therefore, further research should focus on systematic investigations and improvement options, taking a holistic and interdisciplinary approach instead of only working in single fields. Concerted efforts of dairy farmers, researchers, NGOs and political decision makers are necessary to create an economic, ecological and social framework that allows dairy production to serve the entire society. For this, different improvement options should be tested in terms of their impact on environment and income of the farmers, as well as feasibility and sustainability in the peri-urban zones of Faisalabad.

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.

Improving cropping systems of semi-arid south-western Madagascar under multiple ecological and socio-economic constraints

Das Mahafaly Plateau im südwestlichen Madagaskar ist gekennzeichnet durch raue klimatische Bedingungen, vor allem regelmäßige Dürren und Trockenperioden, geringe Infrastruktur, steigende Unsicherheit, hohe Analphabetenrate und regelmäßige Zerstörung der Ernte durch Heuschreckenplagen. Da 97% der Bevölkerung von der Landwirtschaft abhängen, ist eine Steigerung der Produktivität von Anbausystemen die Grundlage für eine Verbesserung der Lebensbedingungen und Ernährungssicherheit in der Mahafaly Region. Da wenig über die Produktivität von traditionellen extensiven und neu eingeführten Anbaumethoden in diesem Gebiet bekannt ist, waren die Zielsetzungen der vorliegenden Arbeit, die limitierenden Faktoren und vielversprechende alternative Anbaumethoden zu identifizieren und diese unter Feldbedingungen zu testen. Wir untersuchten die Auswirkungen von lokalem Viehmist und Holzkohle auf die Erträge von Maniok, der Hauptanbaufrucht der Region, sowie die Beiträge von weiteren Faktoren, die im Untersuchungsgebiet ertragslimitierend sind. Darüber hinaus wurde in der Küstenregion das Potenzial für bewässerten Gemüseanbau mit Mist und Holzkohle untersucht, um zu einer Diversifizierung von Einkommen und Ernährung beizutragen. Ein weiterer Schwerpunkt dieser Arbeit war die Schätzung von Taubildung und deren Beitrag in der Jahreswasserbilanz durch Testen eines neu entworfenen Taumessgerätes. Maniok wurde über drei Jahre und in drei Versuchsfeldern in zwei Dörfern auf dem Plateau angebaut, mit applizierten Zeburindermistraten von 5 und 10 t ha-1, Holzkohleraten von 0,5 und 2 t ha-1 und Maniokpflanzdichten von 4500 Pflanzen ha-1. Maniokknollenerträge auf Kontrollflächen erreichten 1 bis 1,8 t Trockenmasse (TM) ha-1. Mist führte zu einer Knollenertragssteigerung um 30 - 40% nach drei Jahren in einem kontinuierlich bewirtschafteten Feld mit geringer Bodenfruchtbarkeit, hatte aber keinen Effekt auf den anderen Versuchsfeldern. Holzkohle hatte keinen Einfluss auf Erträge über den gesamten Testzeitraum, während die Infektion mit Cassava-Mosaikvirus zu Ertragseinbußen um bis zu 30% führte. Pflanzenbestände wurden felder-und jahresübergreifend um 4-54% des vollen Bestandes reduziert, was vermutlich auf das Auftreten von Trockenperioden und geringe Vitalität von Pflanzmaterial zurückzuführen ist. Karotten (Daucus carota L. var. Nantaise) und Zwiebeln (Allium cepa L. var. Red Créole) wurden über zwei Trockenzeiten mit lokal erhältlichem Saatgut angebaut. Wir testeten die Auswirkungen von lokalem Rindermist mit einer Rate von 40 t ha-1, Holzkohle mit einer Rate von 10 t ha-1, sowie Beschattung auf die Gemüseernteerträge. Lokale Bewässerungswasser hatte einen Salzgehalt von 7,65 mS cm-1. Karotten- und Zwiebelerträge über Behandlungen und Jahre erreichten 0,24 bis 2,56 t TM ha-1 beziehungsweise 0,30 bis 4,07 DM t ha-1. Mist und Holzkohle hatten keinen Einfluss auf die Erträge beider Kulturen. Beschattung verringerte Karottenerträge um 33% im ersten Jahr, während sich die Erträge im zweiten Jahr um 65% erhöhten. Zwiebelerträge wurden unter Beschattung um 148% und 208% im ersten und zweiten Jahr erhöht. Salines Bewässerungswasser sowie Qualität des lokal verfügbaren Saatgutes reduzierten die Keimungsraten deutlich. Taubildung im Küstendorf Efoetsy betrug 58,4 mm und repräsentierte damit 19% der Niederschlagsmenge innerhalb des gesamten Beobachtungszeitraum von 18 Monaten. Dies weist darauf hin, dass Tau in der Tat einen wichtigen Beitrag zur jährlichen Wasserbilanz darstellt. Tageshöchstwerte erreichten 0,48 mm. Die getestete Tauwaage-Vorrichtung war in der Lage, die nächtliche Taubildung auf der metallischen Kondensationsplatte zuverlässig zu bestimmen. Im abschließenden Kapitel werden die limitierenden Faktoren für eine nachhaltige Intensivierung der Landwirtschaft in der Untersuchungsregion diskutiert.

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.