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Abstract: In Huang et al. [17] it was proved that for any Nil d Bohr0-set , there are a minimal system and a non-empty open subset of with , and for any minimal system and any open non-empty , the set is an almost Nil d Bohr0-set. The polynomial form of this problem is considered in this paper. It is shown that the latter is still true in the polynomial case, while the former is not in general. We also consider the special case when the system is a nilsystem. [Copyright &y& Elsevier]

Abstract: In Suzuki (1998) [7] Suzuki gave a classification of association schemes with multiple Q-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzukiʼs theorem mirrors exactly the well-known counterpart for association schemes with multiple P-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980. [Copyright &y& Elsevier]

Abstract: A class of permutation polynomials with given form over finite fields is investigated in this paper, which is a further study on a recent work of Zha and Hu. Based on some particular techniques over finite fields, two results obtained by Zha and Hu are improved and new permutation polynomials are also obtained. [Copyright &y& Elsevier]

This paper is a study on the polynomials over A*-algebras and their useful characterizations. It also contributes to the understanding of the polynomial functions over A*-algebras. [ABSTRACT FROM AUTHOR]

We discuss computability of impressions of prime ends of compact sets. In particular, we construct quadratic Julia sets which possess explicitly described non-computable impressions. [ABSTRACT FROM AUTHOR]

As is well known, the Julia set of Newton's method applied to complex polynomials is connected. The family of König's root-finding algorithms is a natural generalization of Newton's method. We show that the Julia set of König's root-finding algorithms of order s = 3 applied to complex polynomials is not always connected. [ABSTRACT FROM AUTHOR]

Let G be a simple graph. The domination polynomial of a graph G of order n is the polynomial $${D(G,x)=\sum_{i=0}^{n} d(G,i) x^{i}}$$ , where d( G, i) is the number of dominating sets of G of size i. In this article we investigate the domination polynomial at −1. We give a construction showing that for each odd number n there is a connected graph G with D( G, −1) = n. [ABSTRACT FROM AUTHOR]

Let sq(n) denote the sum of the digits in the q-ary expansion of an integer n. In 2005, Melfi examined the structure of n such that s2(n) = s2(n2). We extend this study to the more general case of generic q and polynomials p(n), and obtain, in particular, a refinement of Melfi's result. We also give a more detailed analysis of the special case p(n) = n2, looking at the subsets of n where sq(n) = sq(n2) = k for fixed k. [ABSTRACT FROM AUTHOR]