The Kepler-Bouwkamp constant is defined as the limit of radii of a sequence of concentric circles that are simultaneously inscribed in a regular n-gon and circumscribed around a regular (n + 1)-gon for n ≥ 3. The outermost circle, circumscribed around an equilateral triangle, has radius 1. We investigate what happens when the number of sides of regular polygons from the definition is given by a...

In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in C[x1,x2, . . . ,xn] for n ≥ 3 always form a regular sequence and we state the conjecture when pa, pb, pc for given positive integers a < b < c forms a regular sequence in C[x1,x2,x3,x4]. We also provide evidence for this c...

Let α, β be real numbers and b ≥ 2 be an integer. Allouche and Shallit showed that the sequence {⌊αn+β⌋}n≥0 is b-regular if and only if α is rational. In this paper, using a base-independent regular language, we prove a similar result that the sequence {⌊logb(αn+ β)⌋}n≥0 is b-regular if and only if α is rational. In particular, when α = √ 2, β = 0 and b = 2, we answer the question of Allouche a...

in recent years, many changes have been observed in buying culture of customers and developing chain stores in iran. moreover, need to be more competition in business environments made necessary the stablishment of chain stores, the creation of competitive advantage and long relations to the costumers. regular marketing is a response to stores requirement when establishing such a win-win long r...

This study provides evidence that monkeys are rhythm sensitive. We composed isochronous tone sequences consisting of repeating triplets of two short tones and one long tone which humans perceive as repeating triplets of two weak and one strong beat. This regular sequence was compared to an irregular sequence with the same number of randomly arranged short and long tones with no such beat struct...

In this paper, we study the concept of weakly almost periodic functions on Fréchet algebras. For a algebra [Formula: see text], show that text]. We also text] is Arens regular if and only both are regular. Finally, for sequence algebras prove regualr each

King [3] introduced and examined the concepts of almost A-summable sequence, almost conservative matrix and almost regular matrix. In this paper, we introduce and examine the concepts of λ-almost A-summable sequence, λalmost conservative matrix and λ-almost regular matrix. Also we introduce statistically (V, λ)-summable sequence.