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We introduce near triple arrays as binary row-column designs with at most two consecutive values for the replication numbers of symbols, for the intersection sizes of pairs of rows, pairs of columns and pairs of a row and a column. Near…

We examine a unique construction of the real numbers which proceeds directly from the integers using approximately linear-endomorphisms with finite error, called near-endomorphisms. In this paper, we show that the set of near-endomorphisms…

We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers…

In earlier papers, we showed a decomposition of 2-diregular digraphs (2-dds) and used it to provide some sufficient conditions for these graphs to be non-Hamiltonian; we also showed a close connection between the permanent and determinant…

We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the codewords of a cyclic orbit code and a certain linear set on the projective…

In this paper we investigate $p$-adic self-similar sets and $p$-adic self-similar measures. We show that $p$-adic self-similar sets are $p$-adic path set fractals, and that the converse is not necessarily true. For $p$-adic self-similar…

We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families…

We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental designs and radial basis function approximation. However, it…

We use basic tools of descriptive set theory to prove that a closed set $\mathcal S$ of marked groups has $2^{\aleph_0}$ quasi-isometry classes provided every non-empty open subset of $\mathcal S$ contains at least two non-quasi-isometric…

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…

Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…

We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…

In this paper we provide nearly linear time algorithms for several problems closely associated with the classic Perron-Frobenius theorem, including computing Perron vectors, i.e. entrywise non-negative eigenvectors of non-negative matrices,…

We describe the supercharacter theories of the semidirect product of H and K, $H\rtimes K$ in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce…

Let $R$ be a principal ideal domain (PID). For a simply connected CW-complex $X$ of dimension $n$, let $Y$ be a space obtained by attaching cells of dimension $q$ to $X$, $q>n$, and let $A(Y)$ denote an Adams-Hilton model of $Y$. If…

We discuss non-Abelian discrete R symmetries which might have some conceivable relevance for model building. The focus is on settings with N=1 supersymmetry, where the superspace coordinate transforms in a one-dimensional representation of…

The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.

Let $S_l(M,N)$ denote a set of $\ell$ triples of positive integers having the same sum $M$ and the same product $N$. For each $2\leq\ell\leq 4$ we establish a connection between a subset of $S_l(M,N)$ with (integral) parametric elements and…

Let $ 0\rightarrow \mathfrak{a} \rightarrow \mathfrak{e} \rightarrow \mathfrak{g} \rightarrow 0$ be an abelian extension of the Lie superalgebra $\mathfrak{g}$. In this article we consider the problems of extending endomorphisms of…

The paper introduces new types of nonlinear correlations between bivariate data sets and derives nonlinear auto-correlations on the same data set. These auto-correlations are of different types to match signals with different types of…