‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

Sequences of clicks comprising a dominant regular interval were investigated psychophysically. The first sequence pattern consisted of one regular interclick interval followed by two random intervals. The second sequence pattern consisted of one regular interval with a randomly interspersed click, followed by a single random interval. These stimuli had a single normalized autocorrelation peak o...

It is shown that there exists a sequence of 3-regular graphs {Gn}n=1 and a Hadamard space X such that {Gn}n=1 forms an expander sequence with respect to X, yet random regular graphs are not expanders with respect to X. This answers a question of [NS11]. {Gn}n=1 are also shown to be expanders with respect to random regular graphs, yielding a deterministic sublinear time constant factor approxima...

We construct (k±1)-regular graphs which provide sequences of expanders by adding or substracting appropriate 1-factors from given sequences of kregular graphs. We compute numerical examples in a few cases for which the given sequences are from the work of Lubotzky, Phillips, and Sarnak (with k − 1 the order of a finite field). If k + 1 = 7, our construction results in a sequence of 7-regular ex...

Let X,Y be two sequence spaces defined by speeds of the convergence, i.e.; monotonically increasing positive sequences. In this paper, we give necessary and sufficient conditions for a matrix A (with real or complex entries) to map X into Y. Also analogue well known result Steinhaus, which states that regular cannot transform each bounded convergent sequence, convergence has been proved.

A finite metric space is called here distance degree regular if its sequence the same for every vertex. notion of designs in such spaces introduced that generalizes Q-polynomial distance-regular graphs. An approximation their cumulative distribution function, based on Christoffel function theory given. As an application we derive limit laws weight distributions binary orthogonal arrays strength...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

In this paper, we prove that for every integer k ≥ 1, the k-abelian complexity function of the Cantor sequence c = 101000101 · · · is a 3-regular sequence.

We propose an algorithm for constraint solving over hedges and contexts built over individual, sequence, function, and context variables and flexible arity symbols, where the admissible bindings of sequence variables and context variables can be constrained to languages represented by regular hedge or regular context expressions. We identify sufficient syntactic restrictions that enable to solv...