Point-free Ultrametric Spaces and the Category of Fuzzy Subsets

Some attempts to establish a link between point-free geometry and the categorical approach to fuzzy set theory is exposed. In fact, it is possible to find functors between the category of fuzzy sets as defined by Höhle in [4] and a category whose objects are the pointless ultrametric spaces

Didattica del ragionamento: un esempio di deduzione logica in ambiente Mathematica

Si mostra come, in un ambiente adeguato per il calcolo simbolico, si possano introdurre elementi di programmazione logica, “traducendo” una teoria in un insieme di definizioni di funzioni. Dal punto di vista didattico, tale riduzione della programmazione logica a programmazione funzionale risulta utile per l’ampliamento dell’uso di strumenti informatici all’ambito della logica matematica. Inoltre, un ulteriore obiettivo è quello di facilitare, attraverso tali strumenti, lo sviluppo di competenze non solo nell’ambito del calcolo numerico-algebrico ma anche in quello dell’ informazione di tipo assertivo-logico. Il nostro punto di vista è che nella sperimentazione didattica sia possibile riferirsi alla logica non solo per quanto riguarda il calcolo proposizionale ma anche al suo aspetto deduttivo. E’ necessario evidenziare come il metodo assiomatico sia presente nella vita di tutti i giorni. Nozioni come quelle di “sistema di assiomi” e di “teorema” devono essere interpretate in termini di informazione disponibile, (in generale non completa) circa situazioni della vita reale, e di conseguenze che si possono ricavare a partire da tale informazione

Collective discussions for the development of Interpretative Knowledge in Mathematics Teacher Education

We start from the assumption that teachers need a deep and broad mathematical knowledge —called Interpretative Knowledge (IK)—that allows them to support students in building their mathematical knowledge from their own reasoning and productions. In the present study, we aimed to ascertain how collective discussions focusing on the interpretation of students’ productions engage Prospective Teachers (PTs) and impact their IK development. In particular, we observe how this form of collaborative work among PTs allows for the emergence of novel insights into the mathematical aspects of students’ productions that were not considered during previous individual work, and produce changes in PTs’ attitudes towards students’ productions

Comparison of Iteration Schemes for the Solution of the Multidimensional Schrödinger-Poisson Equations

We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor – corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation ofthe two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor – corrector approach is applied, compared to a corresponding underrelaxation algorithm

Primary teachers’ beliefs and emotional disposition towards mathematics and its teaching

As researches in mathematics education and as teacher educators we are strongly interested in facing the question “what is necessary for teaching mathematics effectively”. The main directions of research emphasize the cognitive side of the answer to this question. In our view, attention from a purely cognitive dimension has to shift to a wider view encompassing also an affective plane, focusing on teachers’ beliefs, emotions and attitudes. We conducted a study to investigate the attitude towards mathematics and its teaching of 189 primary school pre-service teachers. We used as tool a questionnaire composed by questions focused on the three components of attitude (emotional disposition, view, perceived competence), declined along the two dimensions of mathematics and its teaching, according to the TAMT-model. In this paper we discuss some of the results regarding the relationships among the different components of the model with a particular attention to the links among past experiences as students, present, and future perspectives as future teachers

Tracheal obstruction secondary to extravasation of intravenous fluids from a central catheter port

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30358/1/0000760.pd

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabion complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title (February 2009). To appear in Mathematische Annale