Multidimensional wave field signal theory: Mathematical foundations

Multidimensional Wave Field Signal Theory: Transfer Function Relationships

The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz real wavenumber or pseudo-Helmholtz complex wavenumber equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive m...

Mathematical Foundations of Automata Theory

2 Multidimensional Signal Detection Theory

Multidimensional signal detection theory is a multivariate extension of signal detection theory that makes two fundamental assumptions, namely that every mental state is noisy and that every action requires a decision. The most widely studied version is known as general recognition theory (GRT). General recognition theory assumes that the percept on each trial can be modeled as a random sample ...

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.