It has been known for a long time that the sets of integer vectors that are recognizable by finite-state automata are those that can be defined in an extension of Presburger arithmetic. In this paper, we address the problem of deciding whether the closure of a linear transformation preserves the recognizable nature of sets of integer vectors. We solve this problem by introducing an original ext...

The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias [6] states that a compactly supported refinable function in R of finite mask with integer dilation and translations cannot be in C∞. A bound on the regularity based on the eigenvalues of certain matrices associated with the refinement equation is also given. Surprisingly...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

In 1986, Terwilliger showed that there is a strong relation between the eigenvalues of a distance-regular graph and the eigenvalues of a local graph. In particular, he showed that the eigenvalues of a local graph are bounded in terms of the eigenvalues of a distance-regular graph, and he also showed that if an eigenvalue θ of the distance-regular graph has multiplicity m less than its valency k...

Given a finite field F and a positive integer n, we give a procedure to count the n×n matrices with entries in F with all eigenvalues in the field. We give an exact value for any field for values of n up to 4, and prove that for fixed n, as the size of the field increases, the proportion of matrices with all eigenvalues in the field approaches 1/n!. As a corollary, we show that for large fields...

Let A be a nonnegative real matrix which is expanding, i.e. all eigenvalues jj > 1. Suppose that j det(A)j is an integer and let D consists of exactly j det(A)j nonnegative vectors in R n. We classify all pairs (A; D) such that all x in the orthant R n + have at least one radix expansion using base A and digits in D. The matrix A must be a diagonal matrix times a permutation matrix. Also A must...

Let A be a nonnegative real matrix which is expanding i e with all eigenvalues j j and suppose that jdet A j is an integer Let D consist of exactly jdet A j nonnegativevectors inR We classify all pairs A D such that every x in the orthant Rn has at least one radix expansion in base A using digits inD The matrixAmust be a diagonalmatrix times a permutation matrix In addition A must be similar to...