Eduardo Montenegro

GRAPHS r-POLAR SPHERICAL REALIZATIONP

The graph to considered will be in general simple and fi nite, graphs with a nonempty set of edges. For a graph G, V(G) denote the set of vertices and E(G) denote the set of edges. Now, let P r = (0 , 0 , 0 , r ) ∈ R 4 , r ∈ R + . The r − polar sphere, denoted by S P r , is de fi ned by

Una didáctica del saber: un camino hacia la optimización de las transposiciones didácticas.

Resumen es: Preocupados por la educacion de calidad, y dentro del marco de la Teoria de las Situaciones Didacticas (Brousseau, 2004), y particularmente en la aproxim...Worried about the quality of education and within the framework of the Theory of Didactical Situations in Mathematics (Brousseau, 1998), and particularly in the anthropological approach proposed by Yves Chevallard (1991), this paper presents a tool that, in its first place, aims at optimizing the process of didactic transpositions, through the definition of a distance between the knowing how to teach and the knowledge learned (Mabille & Albert, 1994), by proposing the knowledge to be a multidimensional being and each one of these dimensions to be independent from each other. On the other hand, the definition of distance is structured according to a stochastic conception, using the logistic function to model the probability of emitting a correct answer to stimulus acting on the knowledge learned.

ATTRACTORS POINTS IN THE AUTOSUBSTITUTION

Recently an operation of graphs called substitution has been incorporated. In an informal way, the substitution consists in the replacement of a vertex for a graph. This new graph is characterized through a function (of substitution) that it could be self definable. The substitution of each vertex of a graph G, through injectives functions of substitution, by the same G graph will be called autosubstitution and denoted by G(G). If X represents the class of all the simple and finite graphs and w is an application of X in X, defined by w (G) = G(G), then it is interest in studying the dynamic properties of w and the construction of some algorithms that they permit the generating of fractal images. In function of the above-mentioned it is proposed to analyze the autosubstitution for graphs simple and finite. Framed in the area of the Graph Dynamics, inside the area of the Graph Theory, the present work will use, preferably, simple and finite graph.

Didactics on Knowledge: a Road to the Optimization of Didactic Transpositions

Resumen es: Preocupados por la educacion de calidad, y dentro del marco de la Teoria de las Situaciones Didacticas (Brousseau, 2004), y particularmente en la aproxim...Worried about the quality of education and within the framework of the Theory of Didactical Situations in Mathematics (Brousseau, 1998), and particularly in the anthropological approach proposed by Yves Chevallard (1991), this paper presents a tool that, in its first place, aims at optimizing the process of didactic transpositions, through the definition of a distance between the knowing how to teach and the knowledge learned (Mabille & Albert, 1994), by proposing the knowledge to be a multidimensional being and each one of these dimensions to be independent from each other. On the other hand, the definition of distance is structured according to a stochastic conception, using the logistic function to model the probability of emitting a correct answer to stimulus acting on the knowledge learned.

Uma didática do saber: um caminho à optimização das transposições didáticas

Resumen es: Preocupados por la educacion de calidad, y dentro del marco de la Teoria de las Situaciones Didacticas (Brousseau, 2004), y particularmente en la aproxim...Worried about the quality of education and within the framework of the Theory of Didactical Situations in Mathematics (Brousseau, 1998), and particularly in the anthropological approach proposed by Yves Chevallard (1991), this paper presents a tool that, in its first place, aims at optimizing the process of didactic transpositions, through the definition of a distance between the knowing how to teach and the knowledge learned (Mabille & Albert, 1994), by proposing the knowledge to be a multidimensional being and each one of these dimensions to be independent from each other. On the other hand, the definition of distance is structured according to a stochastic conception, using the logistic function to model the probability of emitting a correct answer to stimulus acting on the knowledge learned.

A result about the incident edges in the graphs M k

Abstract Let M k be a graph which is obtained by successive substitutions of k vertices of the complete graph K n , ( k ⩽ n ), by isomorphic copies of the cycle C n −1 . We prove that ‘ M k is hamiltonian’.