Fractal tiles associated with shift radix systems

Shift radix systems form a collection of dynamical systems depending on a parameter $\mathbf{r}$ which varies in the $d$-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters $\mathbf{r}$ these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter $\mathbf{r}$ of the shift radix system, these tiles provide multiple tilings and even tilings of the $d$-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine)

Taxonomic studies of mosses of Seram and Ambon (Moluccas, East Malesia) collected by Indonesian-Japanese botanical expeditions : 9., Pottiaceae

Mosses of Seram and Ambon Islands are reported based on our collections of the botanical expeditions to the islands. This paper is the ninth part of our report and includes the Pottiaceae (total 8 genera and 14 species). One new species, Barbula seramensis H.Akiyama is described

Propagation mechanism of non-uniform distribution of stress and strain in tension test

Elastic-plastic finite element analysis is carried out on tension test to check the uniformity of stress and strain that highly influences the result of numerical analysis in forming processes. Usually stress is calculated by dividing the force by the cross sectional area of the specimen and strain is calculated by the change in a limited gauge length. Basic assumptions are that stress and strain distributions be uniform in the cross section and between two gauge points and the cross section lie between two gauge points. Result of numerical analysis shows that stress and strain distributions are not necessarily uniform especially for those material with poor work hardening ratio. Initiation and propagation of mechanism of this non-uniformity is analyzed to propose a method for a precise measurement of stress and strain

Low Complexity Algorithm for Range-Point Migration-Based Human Body Imaging for Multistatic UWB Radars

High-resolution, short-range sensors that can be applied in optically challenging environments (e.g., in the presence of clouds, fog, and/or dark smog) are in high demand for various applications. Ultrawideband radar is a promising sensor that is suitable for short-range surveillance or watching sensors. Range-point migration (RPM) has been recently established as a promising imaging approach to achieve accurate and real-time 3-D imaging. However, when objects with many scattering points are dealt with, such as a human body, RPM suffers from high computational costs. In this letter, we propose an algorithm with a lower complexity for an RPM-based 3-D imaging method by introducing a sampling-based scattering center extraction with a simplified evaluation function, in which an efficient sample pattern is provided by a golden ratio. The results from a finite-difference time-domain-based numerical test, which introduces a realistic human body object, demonstrate that our proposed method remarkably reduces the computational cost without sacrificing the reconstruction accuracy