Adjacency matrix concepts for the analysis of the interconnection of networks

A mathematical theory is developed for an imagined device termed a “junctor”. A junctor could be used to interconnect two n-terminal networks giving rise to another n-terminal network. Actually a junctor is itself a simple network with three banks of n-terminals internally connected in some fashion by perfectly conducting wires. Adjacency matrices are formulated to analyze various junctors and their current flows. The main problem treated concerns conditions which would ensure that the junctor operation is associative.     

Theory for incompressible fluid turbulence

The functional integral representation for the space-time Hopf characteristic functional associated with boundary-free incompressible fluid turbulence is evaluated accurately to order R^-2, where R is the dimensionless Reynolds number in the theory. This work extends the results obtained previously for C-dominant turbulence to the regime of experimentally accessible large Reynolds numbers. We obtain a characteristic functional of non-Gaussian form as an asymptotically exact solution to the theory for large values of R. Two-point and three-point velocity correlation tensors of physical interest are derived from the characteristic functional.     

Sur l'Acquisition des structures numériques en fin de 3ème

Sans résuméRésultats d'une enquête effectuée en mai-juin 1973 par une équipe de l'IREM de Strasbourg dans les classes de 3ème du Bas-Rhin.L'équipe comprenait quatre membres de l'IREM:Mathématiciens:—Mademoiselle Anne Scherpereel—Monsieur François PluvinagePsychologues:—Mademoiselle Catherine Bloch—Monsieur Raymond Duval.     

Structural aspects of controllability and observability—I. tensorial aggregation

The classical criteria for controllability and observability are given a tensorial formulation which is then extended into Boolean form directly related to a digraph interpretation of system structure. This is examined in detail with particular reference to group theoretic aspects, invariant properties under transformation, the term rank test and the existence of zero eigenvalues.Within this framework the structural design concepts of potential controllability and observability are presented in generalised terms.     

Structural aspects of controllability and Sobservability—II. digraph decomposition

The graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper. Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory.     

Three-axis platform simulation: Bond graph and Lagrangian approach

A bond graph model is derived for the geometric constraints of a three-axis flight table. Gimbal dynamics are easily added even in asymmetrical and unbalanced cases. A method is introduced to make the local dependent inertias computable. The bond graph compares favourably to the Lagrangian approach as to modelling effort and accessibility of intermediate variables as well as having computational advantages.