6 papers
Construction of smooth rhythms through a monotone invariant measure
Fumio Hazama
The present article introduces the notion of quasi-smoothness of marked rhythms through a certain transformation , called reformation map. A marked rhythm consists of a rhythm…
Boolean polynomial expression of the discrete average on the space of rhythms
Fumio Hazama
An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic and combinatorial properties are investi…
Iterative method of construction of good rhythms
Fumio Hazama
On the space of rhythms of arbitrary length with a fixed number of onsets, a self map is constructed. It is shown that for any rhythm of the space there exists a n…
Mathematical Analysis of Melodies: Slope and Discrete Frechet Distance
Fumio Hazama
A directed graph, called an M-graph, is attached to every melody. Our chief concern in this paper is to investigate (1) how the positivity of the slope of the M-graph is related to…
Fixed-Point Problems in Discrete Tomography: Case of Square Windows
Fumio Hazama
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing w…
The moduli space of polygons with area center
Fumio Hazama
A point is said to be an area center of a polygon if all of the triangles composed of and its edges have one and the same area. We construct a moduli space of such $…