相关论文: The Complex of Non-Chromatic Scales

The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…

The aim of this note is a combinatorial description of a category of $D$-modules over an affine space, smooth along the stratification defined by an arrangement of hyperplanes. These $D$-modules are assumed to satisfy certain non-resonance…

This application-oriented study concerns computational musicology, which makes use of grammar systems. We define multi-generative rule-synchronized scattered-context grammar systems (without erasing rules) and demonstrates how to…

Quantification of stylistic differences between musical artists is of academic interest to the music community, and is also useful for other applications such as music information retrieval and recommendation systems. Information about…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

In a recent article, arXiv:2605.12414, it is stated that a certain scale transformation has been "systematically overlooked" in discussions of the tensionless string. Here we point out that this kind of symmetry is treated in numerous…

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces $SL_n(R)/SO(n)$, $SU^*(2n)/Sp(n)$ and their compact duals $SU(n)/SO(n)$…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods…

Arranging music for a different set of instruments that it was originally written for is traditionally a tedious and time-consuming process, performed by experts with intricate knowledge of the specific instruments and involving significant…

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The…

We describe three previously unnoticed components of the moduli space of minimally supersymmetric string theories in $d\geq 7$, describing in some detail their spectrum and duality properties. We find a new component in nine and eight…

We study the harmonic mean of non-zero complex-valued random variables (complex harmonic mean) and establish several geometric estimates and bounds. In contrast to the classical positive-valued case, complex harmonic means may lie outside…

These notes loosely follow an introductory course on graph complexes, held at Humboldt-Universit\"at zu Berlin in summer 23. Instead of simply typing up my lecture notes I decided to give here an overview over (parts of) the topic (lecture…

We study a generalization of the classical Riemannian Tonnetz to N-tone equally tempered scales (for all N) and arbitrary triads. We classify all the spaces that result. The torus turns out to be the most common possibility, especially as N…

We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are…

The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…

We consider a variant of the ring of components of Hurwitz spaces introduced by Ellenberg, Venkatesh and Westerland. By focusing on Hurwitz spaces classifying covers of the projective line, the resulting ring of components is commutative,…

We study the systems of scalar and spinor particles with mixing emitted by external classical sources. The particles wave functions exactly accounting for external sources are obtained directly from the Lorentz invariant wave equations in…