Generating examples: focus on processes

Constructing an example can be a rich and complex activity, interesting to investigate mathematical thinking and with many potentialities in mathematics education. In this article, I analyse processes involved in example generation, with particular emphasis on production and transformation of signs representing mathematical objects and on generation of inferences. The richness and complexity of these processes will also be shown through the notions of prototypes, concept image and concept definition. This investigation reveals aspects that are significant both in education and for the reflection on cognitive and cultural aspects of mathematical thinking.     

Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.     

Mössbauer studies of the Umbria archeological clays

We report an analysis of two different clays from the region of Umbria (Italy): 1. potteries found one inside and the other outside the town of Todi, dating from the end of the IV century B. C., 2. bond clays of Bagnara (Nocera Umbra) and Colfiorito (Foligno) dating V century B.C.     

Synthesis and 1H NMR characterization of substituted 1-amino-9-imino-4-nitro-9,10-dihydr oacridines as potential antitumor agents

A convenient method for the synthesis of unsubstituted and substituted 1-amino-9-imino-4-nitro-9,10-dihydroacridines, 9 and 10 , respectively, is reported. Their ¹H nmr data are reported and discussed in order to confirm the imino tautomeric structure.     

Microstructural changes in irradiated silica based glasses

High voltage electron microscopy studies have been performed on irradiated pure silica and borosilicate glasses to check their long-term stability when these materials are employed near high energy radioactive sources, such as in fusion reactors and during the storage of nuclear waste. The intense energetic beam of electrons produced by the Harwell 1 MeV microscope, ranging from 10¹⁷ to 10²⁰ e/cm²/s has been focused upon specimens of various composition and impurity content at different temperatures up to about 850°C. Pure silica samples have also been bombarded with 46.5 MeV Ni+6 ions at the Variable Energy Cyclotron. It is found that while no significant changes are detectable in pure irradiated silica, clear evidence is present in complex borosilicate glasses for the growing of large defect clusters (over 1000 Å, resembling gas bubbles) after electron doses of about 8.5 × 10¹⁹ e/cm² and dose rates exceeding 2 × 10¹⁸ e/cm²/sec. Moreover, small regions, about 100 Å wide, scattering electrons more than the matrix are also present. The nature of this fine microstructure has been established as a phase separation into crystalline tridymite. The observations are discussed in terms of their dependence on temperature, sample thickness, dose and dose rates.     

Subagging for credit scoring models

The logistic regression framework has been for long time the most used statistical method when assessing customer credit risk. Recently, a more pragmatic approach has been adopted, where the first issue is credit risk prediction, instead of explanation. In this context, several classification techniques have been shown to perform well on credit scoring, such as support vector machines among others. While the investigation of better classifiers is an important research topic, the specific methodology chosen in real world applications has to deal with the challenges arising from the real world data collected in the industry. Such data are often highly unbalanced, part of the information can be missing and some common hypotheses, such as the i.i.d. one, can be violated. In this paper we present a case study based on a sample of IBM Italian customers, which presents all the challenges mentioned above. The main objective is to build and validate robust models, able to handle missing information, class unbalancedness and non-iid data points. We define a missing data imputation method and propose the use of an ensemble classification technique, subagging, particularly suitable for highly unbalanced data, such as credit scoring data. Both the imputation and subagging steps are embedded in a customized cross-validation loop, which handles dependencies between different credit requests. The methodology has been applied using several classifiers (kernel support vector machines, nearest neighbors, decision trees, Adaboost) and their subagged versions. The use of subagging improves the performance of the base classifier and we will show that subagging decision trees achieve better performance, still keeping the model simple and reasonably interpretable.     

Optical efficiency of solar concentrators by a reverse optical path method

A method for the optical characterization of a solar concentrator, based on the reverse illumination by a Lambertian source and measurement of intensity of light projected on a far screen, has been developed. It is shown that the projected light intensity is simply correlated to the angle-resolved efficiency of a concentrator, conventionally obtained by a direct illumination procedure. The method has been applied by simulating simple reflective nonimaging and Fresnel lens concentrators.