A pervasive real-world memory task is remembering to carry out intended activities at appropriate moments in the future, such as remembering to call one’s mother after returning from work or to hand a message to a colleague when seeing him in the office on the next morning. Such types of tasks are termed prospective memory (PM) tasks (Einstein & McDaniel, 1996). PM has been identified as one of the most frequent everyday memory challenges (e.g., Maylor, 1990), particularly in old age (McDaniel, Einstein, & Rendell, 2008) and an intact PM is considered to be crucial for the maintenance of independent living (Kliegel & Martin, 2003). Therefore, many researchers have focused on the exploration of possible age differences in PM. While age-related deficits were found in standard lab-based PM tasks, age-related benefits occured in naturalistic tasks that are carried out in participants’ everyday lives. This surprising pattern has been called the age-PM-paradox (Rendell & Craik, 2000). It has been supported by a meta-analysis comparing PM age effects found in studies that focused either on lab-based or on naturalistic PM tasks (Henry, MacLeod, Phillips, & Crawford, 2004). However, the mechanisms which are critical in determining the direction of age effects remain poorly delineated. Thus, the overall aim of the research programme presented in the present thesis was to investigate the age-PM-paradox as well as potential cognitive, motivational and emotional mechanisms and processes associated with age-related PM performance. For that purpose, three experimental studies were conducted testing adult age effects in different PM task settings with different task material. Furthermore, several possible underlying mechanisms suggested by the literature on age effects in PM were measured and/ or varied experimentally. The first aim of Study 1 was to cross-validate the age-PM-paradox within a single sample. The second aim was to empirically explore the relative importance of four recently proposed factors (motivation, metacognitive awareness, activity absorption, and control over the task) that may be associated with the direction of age effects inside and outside of the laboratory. For that purpose, 20 young and 20 older adults performed a lab-based and a naturalistic PM task, which were similar in structure and demand. The level of control was experimentally manipulated in both task settings. The remaining possibly influencing factors (motivation, metacognitive awareness, and activity absorption) were assessed via questionnaires in the laboratory and with a daily diary in the field. First, analysing mean level age differences, the paradox was confirmed. Second, exploring possible correlates of the paradox revealed that the level of daily activity absorption (i.e., everyday stress) was the most important mechanism in naturalistic PM performance. Further, high motivation and good metacognitive awareness were associated with age benefits in PM performance in the naturalistic task, while high ongoing activity absorption and low control over the PM cue were related to deficits in lab-based tasks. Thus, Study 1 confirmed the age-PM-paradox within one sample and with carefully matched lab-based and naturalistic tasks. In addition, the results indicate that the relative importance of the suggested factors may vary as a function of setting. While cognitive factors were most influential in the laboratory, motivational and knowledge-based factors were associated with high PM performance in the naturalistic task. The strong association between PM performance in the field and everyday stress highlights the need for future studies exploring the mechanisms underlying this effect. Results from Study 1 suggest that cognitive resources are most influential for PM age effects in the laboratory. Yet, it is not clear, which specific cognitive resources are needed for successful PM performance and if these processes differ between young and older adults. Thus, Study 2 explored the role of executive functions (i.e. shifting, updating and inhibition) as possible developmental mechanisms associated with PM age effects. 170 young and 110 older adults performed a battery of cognitive tests including measures of PM, shifting, updating, inhibition, working memory and speed. A comprehensive set of statistical approaches (e.g. median analyses, structural equation modelling) was used to analyze the possible cognitive correlates in predicting PM performance. First, age effects were confirmed in PM and also obtained in measures of executive control. Moreover, the facets of executive control differently predicted PM performance. Specifically, shifting was the strongest predictor of PM performance in young and older adults as well as for explaining age differences in PM. Thus, Study 2 clarified the role of different facets of controlled attention in age effects in PM and bears important conceptual implications: The results suggest that executive functions are important developmental mechanisms of PM across adulthood beyond working memory and speed. Specifically, shifting appeared to be an essential aspect of cognitive control involved in age-related PM performance. Moreover, examining PM as a latent construct confirmed the convergent and discriminant validity of PM. This demonstrates PM as a separate cognitive construct and suggests that PM is related to, but not identical with, executive control. Study 3 was set out to explore if the amount of cognitive resources needed to successfully perform a PM task in the laboratory can be influenced by the emotionality of the task material. First studies suggested that emotional task material may enhance PM performance in young and older adults by heightening the salience of the task and thereby reducing the need for controlled attention. However, the extent and mechanisms of this effect are still under debate. Therefore, Study 3 explored possible differential effects of PM target cue valence on PM age effects. For that purpose, 45 young and 41 older adults performed a PM task in which emotional valence of the PM cue was manipulated (positive, negative, neutral). Results revealed an interaction indicating that age differences were smaller in both emotional valence conditions compared to the neutral condition. This finding supports an emotionally enhanced memory effect in PM, but only for the older adults as PM performance in young adults was not affected by cue valence. From a conceptual perspective, the results from Study 3 may also contribute to the explanation of the age-PM-paradox, as they suggest that the neutral material usually applied in lab-based studies might overestimate PM age effects. In summary, the present thesis makes an important contribution to the ongoing conceptual debate concerning adult age effects in PM performance assessed in the laboratory versus participants’ everyday lives. Results strongly suggest that mostly different variables may be crucial for understanding PM age deficits in the laboratory and age benefits in naturalistic PM tasks. Successful PM performance in the laboratory seems to require high levels of cognitive resources. The present results suggest that shifting ability is especially relevant in this respect. On a task level the emotionality of the material seems to influence the required amount of cognitive resources as it reduced PM age effects. Everyday stress seems to be particularly important for successful PM performance in the field. Thus, possible future studies should specify the relation between stress and PM as outlined in the general discussion.

The concept of function is crucial to a great extent in modern mathematics and is considered a major barrier to many mathematics students. Students have difficulty interpreting information related to functions in general, and quadratic functions in particular. Quadratic Function is one of the topics which are covered in a course which is compulsory for a large number of students in the General Education Program of Zayed University. This program leads to different majors, including Mathematics Education, Business, Information Technology, and other majors. The challenge in teaching Quadratic Function in a course like this is mostly based on the fact that many students think that Quadratic Function is a difficult topic to understand and learn, and some teachers would agree with them that it is difficult to teach. In this paper, I demonstrate real world problems aimed to improve the students understanding of Quadratic Functions; life problems on this topic support developing student’s knowledge, critical thinking, quantitative reasoning, and analytical skills. This paper also includes examples of the techniques used with graphing of quadratic function, the algebra, and inverses of the same function. International move to improve mathematics curriculum have supported new goals for student’s learning which highlights problem solving skills, reasoning, ability to work in groups and individually, and use of technology. Knowing that information technology plays considerable role in achieving the above goals, teaching students the concept of Quadratic Functions can be smoothly achieved by using Information Technology in solving real world problems.

In 1972, professor Grigore Moisil, the most famous Romanian academician for Mathematics, said about Combinatorics, that it is “an opportunity of a renewed gladness”, because “each problem in the domain asks for its solving, an expenditure without any economy of the human intelligence”. More, the research methods, used in Combinatorics, are different from a problem to the other! This is the explanation for the existence of my actual paper, in which I propose to teach Combinatorics, using selected problems. MS classification: 05A05, 97D50.

The development of materials with tailored functionalities and with continuously shrinking linear dimensions towards (and below) the nanoscale is not only going to revolutionize state of the art fabrication technologies, but also the computational methodologies used to model the materials properties. Specifically, atomistic methodologies are becoming increasingly relevant in the field of materials science as a fundamental tool in gaining understanding on as well as for pre-designing (in silico material design) the behavior of nanoscale materials in response to external stimuli. The major long-term goal of atomistic modelling is to obtain structure-function relationships at the nanoscale, i.e. to correlate a definite response of a given physical system with its specific atomic conformation and ultimately, with its chemical composition and electronic structure. This has clearly its pendant in the development of bottom-up fabrication technologies, which also require a detailed control and fine tuning of physical and chemical properties at sub-nanometer and nanometer length scales. The current work provides an overview of different applications of atomistic approaches to the study of nanoscale materials. We illustrate how the use of first-principle based electronic structure methodologies, quantum mechanical based molecular dynamics, and appropriate methods to model the electrical and thermal response of nanoscale materials, provides a solid starting point to shed light on the way such systems can be manipulated to control their electrical, mechanical, or thermal behavior. Thus, some typical topics addressed here include the interplay between mechanical and electronic degrees of freedom in carbon based nanoscale materials with potential relevance for designing nanoscale switches, thermoelectric properties at the single-molecule level and their control via specific chemical functionalization, and electrical and spin-dependent properties in biomaterials. We will further show how phenomenological models can be efficiently applied to get a first insight in the behavior of complex nanoscale systems, for which first principle electronic structure calculations become computationally expensive. This will become especially clear in the case of biomolecular systems and organic semiconductors.

Background. In everyday life it is often required to integrate multisensory input to successfully conduct response inhibition (RI) and thus major executive control processes. Both RI and multisensory processes have been suggested to be altered in autism spectrum disorder (ASD). It is, however, unclear which neurophysiological processes relate to changes in RI in ASD and in how far these processes are affected by possible multisensory integration deficits in ASD. Method. Combining high-density EEG recordings with source localization analyses, we examined a group of adolescent ASD patients (n = 20) and healthy controls (n = 20) using a novel RI task. Results. Compared to controls, RI processes are generally compromised in adolescent ASD. This aggravation of RI processes is modulated by the content of multisensory information. The neurophysiological data suggest that deficits in ASD emerge in attentional selection and resource allocation processes related to occipito-parietal and middle frontal regions. Most importantly, conflict monitoring subprocesses during RI were specifically modulated by content of multisensory information in the superior frontal gyrus. Conclusions. RI processes are overstrained in adolescent ASD, especially when conflicting multisensory information has to be integrated to perform RI. It seems that the content of multisensory input is important to consider in ASD and its effects on cognitive control processes.

Von der Professur Stochastik der Fakultät für Mathematik der Technischen Universität Chemnitz werden seit 1995 regelmäßig jedes Jahr im Herbst die Workshops "Stochastische Analysis" organisiert. Ausgewählte Beiträge sollen erstmals in Form eines Tagungsbandes veröffentlicht werden. Eine jährliche Fortsetzung ist geplant. Der 9. Workshop "Stochastische Analysis" fand vom 29.09.2003 bis zum 01.10.2003 in Bärenstein statt.

Von der Professur Stochastik der Fakultät für Mathematik der Technischen Universität Chemnitz werden seit 1995 regelmäßig jedes Jahr im Herbst die Workshops "Stochastische Analysis" organisiert. Ausgewählte Beiträge werden seit 2003 in Form eines Tagungsbandes veröffentlicht. Der 10. Workshop "Stochastische Analysis" fand vom 27.09.2004 bis zum 29.09.2004 in Klingenthal statt.

Von der Professur Stochastik der Fakultät für Mathematik der Technischen Universität Chemnitz werden seit 1995 regelmäßig jedes Jahr im Herbst die Workshops "Stochastische Analysis" organisiert. Ausgewählte Beiträge werden in Form eines Tagungsbandes veröffentlicht. Der 12. Workshop "Stochastische Analysis" fand vom 20.09.2006 bis zum 22.09.2006 in Schöneck/Vogtland statt.

In praktischen Aufgabenstellungen können zur Modellierung zufälliger Einflüsse, welche sich durch schwache Abhängigkeiten auszeichnen, schwach korrelierte zufällige Funktionen genutzt werden. Die nähere Untersuchung von Funktionalen schwach korrelierter zufälliger Funktionen ist durch die Gestalt der Lösungen von praktischen Fragestellungen motiviert. Die stochastischen Charakteristiken dieser Lösungen lassen sich im Allgemeinen nicht exakt bestimmen, so dass auf Approximationsverfahren zurückgegriffen werden muss. Diese stehen im Mittelpunkt der Dissertation. Zu Beginn werden Entwicklungen von Momenten und Kumulanten der betrachteten linearen Integralfunktionale schwach korrelierter Prozesse nach der Korrelationslänge des Prozesses hergeleitet und eine Vermutung über die exakte Darstellung der Kumulanten formuliert. Für Integralfunktionale von schwach korrelierten Simulationsprozessen, welche aus der Interpolation von Moving-Average-Prozessen entstehen, werden die definierten Charakteristiken hergeleitet. Außerdem steht die Approximation der unbekannten Dichtefunktion im Fokus der Arbeit. Es werden verschiedene Zugänge genutzt. Eine alternative Herleitung zur bereits in der Literatur untersuchten Gram-Charlier-Entwicklung wird in Form der Edgeworth-Entwicklung angegeben. Des Weiteren werden die Sattelpunkt-Approximation und die Maximum-Entropie-Methode untersucht und anhand von Simulationsergebnissen für Integralfunktionale von Simulationsprozessen miteinander verglichen. / In engineering applications stochastic influences which are characterized by weak dependencies can be modelled, among others, by weakly correlated random functions. The solutions of such problems shape up as integral functionals of weakly correlated random functions which motivates more detailed investigations. In general the exact calculation of stochastic characteristics of such integral functionals is impossible so that we have to be content with approximation methods this thesis focuses on. At the beginning expansions of moments and cumulants of linear integral functionals of weakly correlated random processes with respect to the correlation length are considered and an explicit formula of cumulants is conjectured. For integral functionals of weakly correlated random simulation processes, defined as interpolations of moving average processes, the required expansion coefficients are derived. Furthermore the approximation of the unknown probability density is requested. In the thesis there are different approaches used. First we state an alternative way to achieve the already known Gram Charlier approximation by means of Edgeworth expansion. Then we study two further methods, namely the saddlepoint approximation and the maximum entropy method and compare them on the basis of simulation results for integral functionals of simulation processes.

Zur Beschreibung von realen Prozessen werden oft Differentialgleichungen herangezogen. Liegen nun Messdaten von diesen Prozessen vor, so sollen auch die Parameter im mathematischen Modell so gewählt werden, dass diese den Messungen entsprechen. Dieser Vortrag zeigt, wie dies in Mathcad mit der Funktion genfit realisiert werden kann.