On the mathematical foundations of electrical circuit theory

On Mathematical Foundations of the Plausibility Theory

This article constructs a theoretical framework enabling the logic of plausibility to be axiomatised and for decisions about plausibility to be automated. One result is that undecidability presented in the initial theory is resolved. To arrive at a logical-mathematical basis of the theory of plausibility an axiomatization of plausibility logic based on notions of evidence is proposed. It is thr...

On the Mathematical Foundations of Economic Theory

We establish the conditions that must be satisfied for the mathematical operations of linear algebra and calculus to be applicable. The mathematical foundations of the social sciences including economic theory, utility theory, and game theory, depend on these conditions which have not been correctly identified in the classical literature.

Mathematical Foundations of Automata Theory

The Mathematical Foundations of Gauge Theory Revisited

We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies or hydrodynamics, though using the same group theoretical methods and despite the well known couplings existing between elasticity and electromagnetism (piezzoelectricity, photoelasticity, stream...

Foundations of a mathematical theory of darwinism.

This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first t...