The dielectric response of pentagonal defects in multilayer graphene nano-cones has been studied by electron energy loss spectroscopy and ab initio simulations. At the cone apex, a strong modification of the dielectric response is observed below the energy of the π plasmon resonance. This is attributed to π → π* interband transitions induced by topology-specific resonant π bonding states as wel...

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.

A bstract We reconsider a modification of the N -point amplitude Neveu-Schwarz (NS) model in which tachyon becomes pion by shifting its mass to zero and keeping super-projective invariance integrand amplitude. For scattering four particles it reduces written Lovelace Shapiro that has Adler zeroes. confirm also -pion zeroes show non-linear σ -model for α′ → 0 F π fixed. The four- six-point flavo...

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.