Let t=t1t2⋯ be an element of the full shift with map τ on a finite alphabet symbols A and let Σ=closure{τi(t):i∈N∪{0}}. ft=ft1,∞=⋯∘ft2∘ft1 non-autonomous system over compact metric space X where ti∈A. The set Ft+={fτi(t):i∈N} is called shifted family ft. If t transitive in AN, then Ft+‾ classical IFS; otherwise, Σ subshift Ft+‾={fσ=fσ1,∞:σ∈Σ} “generalized” IFS. We show that if ft has some shado...

The σ -convergence and σ -core of a real bounded sequence were introduced in [R. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963) 81–94] and [S.L. Mishra, B. Satapathy, N. Rath, Invariant means and σ -core, J. Indian Math. Soc. 60 (1984) 151–158], respectively. In this work, we extend these ideas to double sequences. c © 2006 Elsevier Ltd. All rights r...

For a given closed oriented surface Σ, we introduce chord index homomorphism from subgroup of H1(Σ,Z) to the group indices knot K in Σ×I. Some invariants derived this are discussed.

In this paper, we investigate those positive integers n for which the equality σ(φ(n)) = σ(n) holds, where σ is the sum of the divisors function and φ is the Euler function.