A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic

An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.     

Monitoring the packet gap of real-time packet traffic

Real-time packet traffic is characterized by a strict deadline on the end-to-end time delay and an upper bound on the information loss. Due to the high correlation among consecutive packets, the individual packet loss does not well characterize the performance of real-time packet sessions. An additional measure of packet loss is necessary to adequately assess the quality of each real-time connection. The additional measure considered here is the average number of consecutively lost packets, also called the average packet gap. We derive a closed form for the average packet gap for the multiclassG/G/m/B queueing system in equilibrium and show that it only depends on the loss behavior of two consecutive packets. This result considerably simplifies the monitoring process of real-time packet traffic sessions. If the packet loss process is markovian, the consecutive packet loss has a geometric distribution.     

Hyperelliptic parametrizations of $$\pmb {\mathbb {Q}}$$ Q -curves

The Ramanujan Journal - In this paper, our aim is to find the radii of starlikeness and convexity of the Ramanujan type function for three different kinds of normalization by using their...     

Banzhaf Measures for Games with Several Levels of Approval in the Input and Output

An axiomatic characterization of ‘a Banzhaf score’ notion is provided for a class of games called (j,k) simple games with a numeric measure associated to the output set, i.e., games with n players, j ordered qualitative alternatives in the input level and k possible ordered quantitative alternatives in the output. Three Banzhaf measures are also introduced which can be used to determine a player's ‘a priori’ value in such a game. We illustrate by means of several real world examples how to compute these measures. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

The index of a plane curve and green’s formula

In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green’s formula with multiplicities that involves the of the function and the index of the cycle. We consider this formula in several settings and we obtain a sharp version in terms of the Lebesgue integrability properties of the partial derivatives of the function. This result depends on the proven fact that the index of a rectifiable cycle is square integrable with respect to the planar Lebesgue measure. The work of both authors is partially supported by grants 2000SGR-00059, 2001SGR 00172 of Generalitat de Catalunya and BFM 2002-04072-C02-02 of Ministerio de Ciencia y Tecnologia     

How to avoid the cheaters succeeding in the key sharing scheme

In this paper the Rational Interpolation is presented as a solution to the problem caused by a cheater using the Threshold Scheme. We will implement this scheme by using the Berlekamp-Massey algorithm.The first version we present does not try to detect the cheaters, as in [3], [9] or [10]. This version tries to prevent their knowledge of the correct keyD while the other participants are aware only of the false keyD computed in the threshold scheme.The second version we present is to detect the existence of cheaters.This work was partially supported by Spanish CICYT Grant TIC91-0472.     

Quasi-Hadamard Full Propelinear Codes

In this paper, we give a characterization of quasi-Hadamard groups in terms of propelinear codes. We define a new class of codes that we call quasi-Hadamard full propelinear codes. Some structural properties of these codes are studied and examples are provided.     

On the 2-adic valuation of the cardinality of elliptic curves over finite extensions of $$\mathbb {F}_{\varvec{q}} $$

In this paper we study the difference between the 2-adic valuations of the cardinalities \( \# E( \mathbb {F}_{q^k} ) \) and \( \# E( \mathbb {F}_q ) \) of an elliptic curve E over \( \mathbb {F}_q \). We also deduce information about the structure of the 2-Sylow subgroup \( E[ 2^\infty ]( \mathbb {F}_{q^k} ) \) from the exponents of \( E[ 2^\infty ]( \mathbb {F}_q ) \).