Producing an explanatory proof in a 9th grade classroom

Este artigo apresenta parte de um estudo fundamentado na problemática da demonstração na matemática escolar. Descreve o modo como quatro alunos do 9.º ano exploraram uma tarefa relacionada com a descoberta de eixos de simetria em várias figuras geométricas. A demonstração, que os mesmos construíram, teve essencialmente uma função explicativa. O papel da professora na negociação do significado de demonstração e da sua necessidade é igualmente analisado. Os alunos desenvolvem primeiro uma compreensão prática sem consciência das razões que fundamentam as afirmações matemáticas e só depois uma compreensão teórica que os conduz à construção de uma demonstração.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Who Is Influential and Why? The Determinants of Reputational Power

Power is one of the most fundamental concepts in political science, and it is a crucial aspect of decision-making structures. The distribution of power between political actors and coalitions of actors informs us about who is actually able to influence decision-making processes. It is thus no surprise that power is a centerpiece of our assessment of political decision-making in Switzerland. In line with the main argument of this book, Chapter 3 has uncovered important changes in decision-making structures, which resulted in a rebalancing of power between governing parties, interest groups and state executive actors. Conjecturing about the reasons that may account for these changes, we pointed to factors of an organizational and institutional nature. For example, we put forward the decline of pre-parliamentary procedures oriented towards corporatist intermediation as a possible explanation for the weakening of interest groups. More generally, in several chapters it has been suggested that there is a relationship between the institutional design of a decision-making process, the related importance of decision-making phases and an actor's participation in these phases on the one hand, and the power of actors (and coalitions of actors) on the other. In addition, the analyses carried out in Chapters 2 to 5 draw our attention to the differences in power structure across decision-making processes or types of processes.