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The aim of this article is to discuss and clarify the notion of fractality for subgroups of the group of automorphisms of a regular rooted tree. For this purpose we define three types of fractality. We show that they are not equivalent, by…
Chord recognition serves as a critical task in music information retrieval due to the abstract and descriptive nature of chords in music analysis. While audio chord recognition systems have achieved significant accuracy for small…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
It is well known that a straight Nambu-Goto string is an exact solution of the equations of motion when its end moves in a circular orbit. In this paper we investigate the shape of a confining relativistic string for a general motion of its…
Acoustic metafluids are defined as the class of fluids that allow one domain of fluid to acoustically mimic another, as exemplified by acoustic cloaks. It is shown that the most general class of acoustic metafluids are materials with…
Variational design is a well-recognized CAD technique due to the increased design efficiency. It often presents as a parametric family of CAD models. Although effective, this way of working cannot handle design requirements that go beyond…
It is well known that acoustic fields can produce forces on single particles, however they can also induce inter-particle forces due to multiple scattering events. This multi-particle force -- here referred to as acoustic binding -- is…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or…
In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroup of [7]. Several…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
We consider a class of conformal models describing closed strings in axially symmetric stationary magnetic flux tube backgrounds. These models are closed string analogs of the Landau model of a particle in a magnetic field or the model of…
We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfister forms. We establish "going-up" results for group and…
Straight cylindrical stethoscopes serve as an important alternative to conventional stethoscopes whose application in the treatment of infectious diseases might be limited by the use of protective clothing. Yet their miniaturization is…
Context. A porous and/or fractal description can generally be applied where particles have undergone coagulation into aggregates. Aims. To characterise finite-sized, porous and fractal particles and to understand the possible limitations of…
In the process of developing a new digital music interface, the author faced three questions that have attracted little to no attention in the literature. By tracking body joints, a performer can use body parts to directly control a digital…
This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…