Fundamental Notions in Vector Analysis

Conceptual Graphs: fundamental notions

We state precise definitions of the basic notions of Sowa’s framework [Sowa 84] and provide related results. These results mainly concern the structure of the specialization relation, correspondence between graph operations and logical operations, and algorithmic complexity of the model handling. RESUME. Nous définissons précisément les notions de base du modèle des graphes conceptuels de Sowa ...

Fundamental notions of analysis in subsystems of second-order arithmetic

We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships betwe...

Defending liquidity preference and Keynesian notions of fundamental uncertainty

Affine and fundamental vector fields

This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in a bijective correspondence with the fundamental vector fields on it of respectively general affine, general linear and translation groups (locally) represent...

Analysis of Notions of Diagnosis

Various formal theories have been proposed in the literature to capture the notions of diagnosis underlying diagnostic programs. Examples of such notions are: heuristic classification, which is used in systems incorporating empirical knowledge, and model-based diagnosis, which is used in diagnostic systems based on detailed domain models. Typically, such domain models include knowledge of causa...