Traditional rough set theory is only suitable for dealing with discrete variables and need data preprocessing. Neighborhood rough sets overcome these shortcomings with the ability to directly process numeric data. This paper modifies the attribute reduction method based on neighborhood rough sets, in which the attribute importance is combined with information entropy to select the appropriate a...

We analyze all orthonormal bases of exponentials on the Cantor set defined by Jorgensen and Pedersen in J. Anal. Math. 75,1998, pp 185-228. A complete characterization for all maximal sets of orthogonal exponentials is obtained by establishing a one-to-one correspondence with the spectral labelings of the infinite binary tree. With the help of this characterization we obtain a sufficient condit...

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let U g n be the set of unicyclic graphs of order n with girth g. For all integers n and g with 5 ≤ g ≤ n − 6, we determine the first ⌊ g2⌋+ 3 spectral radii of unicyclic graphs in the set U g n .

This paper considers a parametrization of a class of J spectral factors of a given J spectral density. The notion of J stable functions is introduced to define a partial ordering on the set of J spectral factors. Necessary and sufficient conditions for the existence of extremal J spectral factors are given and a number of explicit factorization results is derived which serve for the algorithmic...

A Borel measure μ in R is called a spectral measure if there exists a set Λ ⊂ R such that the set of exponentials {exp(2πiλ · x) : λ ∈ Λ} forms an orthogonal basis for L(μ). In this paper we prove some properties of spectral measures. In particular, we prove results that highlight the 3/2-rule.

We present techniques for spectral image acquisition. The spectral domain of the images is represented by a lowdimensional component image set, which is used to obtain an efficient compression of the high-dimensional spectral data. First, computational techniques to design color filters with a constraint of positive spectral values is described. Then, we present two prototypes of our spectral i...

In order to recover spectral reflectances or transmittances using a multispectral imaging based technique, it is necessary to know the spectral radiance of the illuminant used to light the samples in the acquisition process. In this study, we analyzed the influence of the spectral distribution of the illuminant on the reconstruction of spectral reflectances in the near infrared region of the sp...

We compute burst spectra and time structures arising from synchrotron and inverse Compton scattering by non-thermal electrons accelerated in shocks which form during the interaction between a thin ultra-relativistic fireball and a stationary external medium. We investigate the effect of varying the most important model parameters on the resulting burst spectra, and we present a set of correlati...

In this paper, we prove the Tiling implies Spectral part of Fuglede’s cojecture for the three interval case. Then we prove the converse Spectral implies Tiling in the case of three equal intervals and also in the case where the intervals have lengths 1/2, 1/4, 1/4. Next, we consider a set Ω ⊂ R, which is a union of n intervals. If Ω is a spectral set, we prove a structure theorem for the spectr...