Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

World Hunger, Malnutrition and Brain Development of Children

Hunger is still a major problem faced by people in the world especially in some areas in developing countries, and this condition is a cause of undernutrition. Insufficient nutrition during the early stages of life may adversely influence brain development. It was observed from my own research conducted in Bogor, Indonesia, that children with severe acute malnutrition (SAM, body mass index or BMI for age z score < -3) (N=54) had significantly (p<0.05) lower memory ability score (46.22±1.38) compared to normal children (BMI for age z score -2 ≤ z ≤ 1) (N=91) (51.56±1.24). Further, children with Moderate Acute Malnutrition (MAM, BMI for age z score -3 ≤ z <-2) tended to (p<0.1) have lower memory ability (50.08±1.58) than the normal children. On the other hand, overnutrition among children also might impair the brain function. The study revealed that children who are overweight (BMI for age z score 1 < z ≤ 2) (N=8) significantly (p<0.05) had lower memory ability score (46.13±4.50) compared to the normal children. This study also revealed that obese children (BMI for age z score > 2) (N=6) tended to (p<0.1) have lower memory ability score (50.33±5.64) than the normal children. It is therefore very important to maintain children at a normal BMI, not being undernourished (SAM and MAM categories) on one side and not being overnourished (overweight and obesity categories) on the other side in order to optimise their brain development. This could be achieved through providing children with an adequate and balanced nutrient supply via food.

Ist der Ernährungsführerschein eine geeignete Primärpräventionsmaßnahme, um die Ernährungssituation zu verbessern?

Das Ernährungsverhalten einer Bevölkerung hat einen wesentlichen Einfluss auf das Wohlbefinden, die Gesundheit und Leistungsfähigkeit der Menschen. Ernährungsbedingte, chronische Erkrankungen weisen in den westlichen Industrienationen eine hohe Inzidenz und Prävalenz auf. Präventionsmaßnahmen im Setting Schule sollen das Ernährungsverhalten der Kinder- und Jugendlichen positiv beeinflussen. Gerade in diesem Setting können Personen mit unterschiedlichem sozioökonomischem Status, sowie Personen aus diversen Lebensbereichen angesprochen werden. Der Ernährungsführerschein (EFS) ist eine schulbasierte Primärpräventions-maßnahme, der in der 3. Jahrgangsstufe/Grundschule durchgeführt wird. In 6 – 7 Unterrichtseinheiten erfolgt eine praxisnahe Vermittlung von Grundkenntnissen über Ernährung, Lebensmittel und deren Zubereitung. Der EFS möchte eine Verhaltensänderung der Schulkinder bewirken. Sie erlernen Kompetenzen, damit sie in der Lage sind, sich selbst eine gesunde Mahlzeit zubereiten zu können. Aber kann dieses Projekt eine nachhaltige Verhaltensänderung bewirken? Die folgende Studie mit Mixed-Methods-Ansatz im Explanatory-Sequential-Design versucht genau dieser Frage nachzugehen. Auf eine quantitative Prä- und Postbefragung in 16 Klassen an 12 Grundschulen im Landkreis Marburg Biedenkopf und insgesamt 992 Befragungen folgte eine qualitative Studie mit neun problemzentrierten, leitfadengestützten Interviews. Der EFS zeigt keinen signifikanten Einfluss auf die Veränderung des Ernährungsverhaltens. Positiv zu bewerten ist, dass durch den EFS Alltagskompetenzen bei der Nahrungszubereitung gefördert wurden. Dieser positive Einfluss muss jedoch differenziert betrachtet werden, denn die qualitativen Studie zeigt, dass der EFS sehr gut in Familien aufgenommen wird, die sich bereits mit Ernährungsfragen auseinandersetzen und darauf achten, einen ernährungsphysiologisch günstigen Ernährungsstil zu leben oder anzustreben. In Familien der Billig- und Fleischesser konnte der EFS die Türen nicht öffnen. Aber gerade in diesem Segment wäre eine Veränderung des Essverhaltens induziert. Die Untersuchung ergab, dass der EFS für sich alleine nicht den Anspruch erheben kann, die Ernährungssituation der Kinder und Familien zu verbessern. Aber er bietet ein methodisch-didaktisch gut ausgearbeitetes Konzept und könnte als Baustein in die Entwicklung eines praxisnahen, erlebnisorientierten und ganzheitlichen Ernährungsbildungskonzepts unter Berücksichtigung diverser Settings und Lebenswelten der Kinder und Familien einfließen.

Double burden malnutrition of preschool children and its association with brain development and milk consumption

Protecting the quality of children growth and development becomes a supreme qualification for the betterment of a nation. Double burden child malnutrition is emerging worldwide which might have a strong influence to the quality of child brain development and could not be paid-off on later life. Milk places a notable portion during the infancy and childhood. Thus, the deep insight on milk consumption pattern might explain the phenomenon of double burden child malnutrition correlated to the cognitive impairments. Objective: Current study is intended (1) to examine the current face of Indonesian double burden child malnutrition: a case study in Bogor, West Java, Indonesia, (2) to investigate the association of this phenomenon with child brain development, and (3) to examine the contribution of socioeconomic status and milk consumption on this phenomenon so that able to formulate some possible solutions to encounter this problem. Design: A cross-sectional study using a structured coded questionnaire was conducted among 387 children age 5-6 years old and their parents from 8 areas in Bogor, West-Java, Indonesia on November 2012 to December 2013, to record some socioeconomic status, anthropometric measurements, and history of breast feeding. Diet and probability of milk intake was assessed by two 24 h dietary recalls and food frequency questionnaire (FFQ). Usual daily milk intake was calculated using Multiple Source Method (MSM). Some brain development indicators (IQ, EQ, learning, and memory ability) using Projective Multi-phase Orientation method was also executed to learn the correlation between double burden child malnutrition and some brain development indicator. Results and conclusions: A small picture of child double burden malnutrition is shown in Bogor, West Java, Indonesia, where prevalence of Severe Acute Malnutrition (SAM) is 27.1%, Moderate Acute Malnutrition (MAM) is 24.9%, and overnutrition is 7.7%. This phenomenon proves to impair the child brain development. The malnourished children, both under- and over- nourished children have significantly (P-value<0.05) lower memory ability compared to the normal children (memory score, N; SAM = 45.2, 60; MAM = 48.5, 61; overweight = 48.4, 43; obesity = 47.9, 60; normal = 52.4, 163). The plausible reasons behind these evidences are the lack of nutrient intake during the sprout growth period on undernourished children or increasing adiposity on overnourished children might influence the growth of hippocampus area which responsible to the memory ability. Either undernutrition or overnutrition, the preventive action on this problem is preferable to avoid ongoing cognitive performance loss of the next generation. Some possible solutions for this phenomenon are promoting breast feeding initiation and exclusive breast feeding practices for infants, supporting the consumption of a normal portion of milk (250 to 500 ml per day) for children, and breaking the chain of poverty by socioeconomic improvement. And, the national food security becomes the fundamental point for the betterment of the next. In the global context, the causes of under- and over- nutrition have to be opposed through integrated and systemic approaches for a better quality of the next generation of human beings.

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.