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.

Effects of red brick production on land use, household income, and greenhouse gas emissions in Khartoum, Sudan

In Khartoum (Sudan) a particular factor shaping urban land use is the rapid expansion of red brick making (BM) for the construction of houses which occurs on the most fertile agricultural Gerif soils along the Nile banks. The objectives of this study were to assess the profitability of BM, to explore the income distribution among farmers and kiln owners, to measure the dry matter (DM), nitrogen (N), phosphorus (P), potassium (K) and organic carbon (C_org) in cow dung used for BM, and to estimate the greenhouse gas (GHG) emissions from burned biomass fuel (cow dung and fuel wood). About 49 kiln owners were interviewed in 2009 using a semi-structured questionnaire that allowed to record socio-economic and variable cost data for budget calculations, and determination of Gini coefficients. Samples of cow dung were collected directly from the kilns and analyzed for their nutrients concentrations. To estimate GHG emissions a modified approach of the Intergovernmental Panel on Climate Change (IPCC) was used. The land rental value from red brick kilns was estimated at 5-fold the rental value from agriculture and the land rent to total cost ratio was 29% for urban farms compared to 6% for BM. The Gini coefficients indicated that income distribution among kiln owners was more equal than among urban farmers. Using IPCC default values the 475, 381, and 36 t DM of loose dung, compacted dung, and fuel wood used for BM emit annually 688, 548, and 60 t of GHGs, respectively.

Employment and Income of Workers on Indonesian Oil Palm Plantations: Food Crisis at the Micro Level

The importance of oil palm sector for Indonesia is inevitable as the country currently serves as the world’s largest producer of crude palm oil. This paper focuses on the situation of workers on Indonesian oil palm plantations. It attempts to investigate whether the remarkable development of the sector is followed by employment opportunities and income generation for workers. This question is posed within the theoretical framework on the link between trade liberalisation and labour rights, particularly in a labour-intensive and low-skilled sector. Based on extensive field research in Riau, this paper confirms that despite the rapid development of the oil palm plantation sector in Indonesia, the situations of workers in the sector remain deplorable, particularly their employment status and income. This also attests that trade liberalisation in the sector adversely affects labour rights. The poor working conditions also have ramifications for food security at the micro level.

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.

Poverty targeting and income impact of subsidised credit on accessed households in the Northern Mountainous Region of Vietnam

This paper uses the data of 1338 rural households in the Northern Mountainous Region of Vietnam to examine the extent to which subsidised credit targets the poor and its impacts. Principal Component Analysis and Propensity Score Matching were used to evaluate the depth of outreach and the income impact of credit. To address the problem of model uncertainty, the approach of Bayesian Model Average applied to the probit model was used. Results showed that subsidised credit successfully targeted the poor households with 24.10% and 69.20% of clients falling into the poorest group and the three bottom groups respectively. Moreover, those who received subsidised credit make up 83% of ethnic minority households. These results indicate that governmental subsidies are necessary to reach the poor and low income households, who need capital but are normally bypassed by commercial banks. Analyses also showed that ethnicity and age of household heads, number of helpers, savings, as well as how affected households are by shocks were all factors that further explained the probability at which subsidised credit has been assessed. Furthermore, recipients obtained a 2.61% higher total income and a 5.93% higher farm income compared to non-recipients. However, these small magnitudes of effects are statistically insignificant at a 5% level. Although the subsidised credit is insufficient to significantly improve the income of the poor households, it possibly prevents these households of becoming even poorer.