The Jost solutions and the scattering matrix function are constructed explicitly for the Dirac type system on the axis in the case of the rectangular matrix pseudo-exponential potentials. It is shown that the evolution of these potentials is related to the matrix soliton-positon interaction. The...

Let 1 be a Pisot unit. A family of sets {} defined by -expansion has been extensively studied as atomic surface or Rauzy fractal. For the purpose of constructing Markov partition, a domain constructed by atomic surface has appeared in several literature [10, 7, 14]. In this paper we show that...

Let Ω be a smooth bounded domain in . Assume that ≥ 0 is a -function on [0, ∞) such that ()/ is increasing on (0, +∞). Let be a real number and let ≥ 0, ≢ 0 be a continuous function such that ≢ 0 on ∂Ω. The purpose of this Note is to establish the asymptotic behaviour of the...

A Pisot unit substitution defines a graph-directed iterated function system (graph-IFS in short), and the invariant sets are called atomic surfaces. The graph-IFS of atomic surfaces is represented by a dual substitution on stepped-surfaces, and the study of the graph-IFS is transfered to that of...

Let ∑ be a Seifert fibered homology sphere and τ the complex conjugation involution on ∑ viewed as a link of singularity. We study the equivariant topology of (2) representation space of π(Σ) with respect to the involution induced by τ. As an application we prove splicing additivity in...

The recently introduced Reverse Jacket matrix (RJM) has a generalized form of the Hadamard matrix. Thus the RJM is closely related to the matrix for a fast Fourier transform (FFT). It also has a very interesting structure, i.e., its inverse can be easily obtained and has the reversal form of the...

The comparison of a power of general goodness-of-fit tests of the Pearson's, the Kolmogorov-Smirnov's and of the author of the present paper has been presented.It is shown that for distributions like simular to exponential, the goodness-of-fit test of the author is locally the most powerful. The...

The paper presents the equations of average human lifetime specifying its dependence on the absorbed dose and dosa rate. Based on these equation, the influence of various components of ionizing radiation on human lifetime has been determined.In addition, the equations of average mice lifetime of...