The five papers that comprise this special issue entitled ‘‘The conceptual change approach to mathematics learning and teaching,’’ attempt to demonstrate that the conceptual change approach can be a fruitful component of a theory of mathematical learning and instruction. Some of them focus on issues of learning i.e., on presenting evidence that the conceptual change approach provides a powerful...

We investigate the relation between two quantitative measures characterizing short term memory in input driven dynamical systems, namely the short term memory capacity (MC) [2] and the Fisher memory curve (FMC) [1]. We show that under some assumptions, the two quantities can be interpreted as squared ‘Mahalanobis’ norms of images of the input vector under the system’s dynamics and that even tho...

Der folgende Artikel gibt einen Kurzüberblick über ein Promotionsvorhaben im Bereich der Quantitativen Modellierung. In der Dissertation soll die Modellierungsmethodik FMC-QE (Fundamental Modeling Concepts for Quantitative Evaluation) beschrieben werden. FMC-QE basiert auf der Modellierungssprache FMC sowie den Modellierungsund Berechnungsmethoden der Warteschlangentheorie und der Zeitbehaftete...

Teaching mathematics in a high school and in a community college in the New York City, I have noticed that students grasp mathematical concepts more quickly and understand them better when a connection between the concept and the world of business is established. Students were visibly more interested and involved when business applications were presented first, laying the groundwork for technol...

Fixed–mobile convergence (FMC) is a radical innovation for telecommunication companies because it requires them to move into unknown territories that are beyond traditional business lines and underlying technologies. In the meantime, understanding what types of telecommunication companies are better at doing business through the early adoption of FMC has become increasingly important in the con...

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in te...

This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for ...

We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the KalaiSmorodinsky solution always finishes o...

This thesis studies axiomatic and computational aspects of set-valued solution concepts in social choice and game theory. It is divided into two parts. The first part focusses on solution concepts for normal-form games that are based on varying notions of dominance. These concepts are intuitively appealing and admit unique minimal solutions in important subclasses of games. Examples include Sha...