UNA METAFISICA PITAGORICA NEL FILERO?

The present essay will cross, inside the matter of the sources of the platonic thought, the suggestion of Damascius of Damascus, with the intention to draw clear understanding, unless in this particular point, of the relationship between the ancient pythagoreanism and the platonic philosophy. In this, the study of the matter of the dialectics of the limiters/unlimited one is central. The page 16c of the Philebus is the crucial point of this discussion: here Socrates introduces the theme of the unity/multiplicity as a very beautiful hodos, a run that comes from a very distant point of departure: it’s a “gift of the gods” and a discovery of the ancient ones. The comparative study of these footsteps of the Philebus and the fragments of Philolaus, especially В 2, 3, 6 and 7 bring us to conclude that the presence in the pages of the Philebus of the theory of the limiter/unlimited be taken as a pre-platonic “discovery” of the more ancient pythagorean philosophy.

THE ACCURACY OF LEAST-SQUARES APPROXIMATION ON HIGHLY STRETCHED MESHES

The least-squares (LS) method is often used in computational aerodynamics to reconstruct a given function at certain points of a computational grid. In this paper we discuss the accuracy of the LS approximation on highly stretched meshes that are inherent in computational aerodynamics. A new definition of a distant point in a LS reconstruction stencil will be given in order to explain the poor performance of the method in a boundary layer region. Namely, based on the concept of outliers widely used in the statistics, we demonstrate that the definition of a distant point in a LS reconstruction stencil should take into account the solution properties and it cannot rely upon the geometric shape of the stencil only. Our approach is illustrated with numerical examples.