Related papers: Axiomatic Music Theory
A phonon theory of precursor phenomena in martensitic phase transformations is developed. Extending Gr\"uneisen theory of thermal expansion, this theory addresses the effects of deformation-dependent low-energy phonons on the structural,…
We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.
Perhaps one of the most intriguing questions in philosophy concerns the true nature of external reality. In this paper, we discuss some of the theories that have been put forth regarding the nature of reality and of our perceived universe.…
This is a research announcement of the theory of orbifold quantum cohomology.
Traditional approaches to combination tones based on Helmholtz theory encounter essential interpreting difficulties, which the most known example is the anomalous behaviour of the combination tone 2f1-f2. Without doubt the phenomenon of…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
In this monograph, very simple axiomatic definitions to the L. Schwartz' concepts of distribution and derivative of a distribution are formulated. Beyond this, a kind of generalization of that concepts is propose and corresponding axiomatic…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
String theory is the most promising candidate theory for a unified description of all fundamental forces exist in the nature. It provides a mathematical framework that combine quantum theory with Einstein's general theory of relativity. But…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
Answering a question of Kaye, we show that the compositional truth theory with a full collection scheme is conservative over Peano Arithmetic. We demonstrate it by showing that countable models of compositional truth which satisfy the…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
This Thesis discusses the development of technologies for the automatic resynthesis of music recordings using digital synthesizers. First, the main issue is identified in the understanding of how Music Information Processing (MIP) methods…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Music is a potent form of expression that can communicate, accentuate or even create the emotions of an individual or a collective. Both historically and in contemporary experiences, musical expression was and is commonly instrumentalized…
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional…