On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space

Recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed spaces by Mursaleen and Mohiuddine [Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, Solitons Fractals, 41 (2009) pp. 2414-2421]. We know that ideal convergence is more general than statistical convergence for single or double sequences. This has motivated us to study the ideal convergence of double sequences in a more general setting. That is, in this paper, we study the concept of ideal convergence and ideal Cauchy for double sequences in intuitionistic fuzzy normed spaces.

On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces

Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons & Fractals 2006;27:331–44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons & Fractals 2008;35:763–69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.

Statistical convergence of double sequences in intuitionistic fuzzy normed spaces

In this paper, we define and study λ -statistical convergence in intuitionistic fuzzy normed spaces (IFNS) which provide little better tool to study a more general class of sequences. We also introduce here a new concept, that is, λ -statistical completeness and show that IFNS is λ -statistically complete but not complete.

On generalized statistical convergence in intuitionistic fuzzy normed space

In this paper, we determine some stability results concerning the cubic functional equation f ( 2 x + y ) + f ( 2 x - y ) = 2 f ( x + y ) + 2 f ( x - y ) + 12 f ( x ) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the cubic mappings and prove that the existence of a solution for any approximately cubic mapping implies the completeness of IFNS.

On stability of a cubic functional equation in intuitionistic fuzzy normed spaces

Random hopping among localized states and charge fluctuation at disordered surfaces

Tungsten (W) is considered to be the most promising plasma-facing material in fusion reactors. During their service, severe irradiation conditions create plenty of point defects in W, which can significantly degrade their performance. In this work, we first employ the molecular static simulations to investigate the interaction between a 1/2[111] dislocation loop and a vacancy-type defect including a vacancy, di-vacancy, and vacancy cluster in W. The distributions of the binding energies of a 1/2[111] interstitial and vacancy dislocation loop to a vacancy along different directions at 0 K are obtained, which are validated by using the elasticity theory. The calculated distributions of the binding energies of a 1/2[111] interstitial dislocation loop to a di-vacancy and a vacancy cluster, showing a similar behavior to the case of a vacancy. Furthermore, we use the molecular dynamics simulation to study the effect of a vacancy cluster on the mobility of the 1/2[111] interstitial dislocation loop. The interaction is closely related to the temperature and their relative positions. A vacancy cluster can attract the 1/2[111] interstitial dislocation loop and pin it at low temperatures. At high temperatures, the 1/2[111] interstitial dislocation loop can move randomly. These results will help us to understand the essence of the interaction behaviors between the dislocation loop and a vacancy-type defect and provide necessary parameters for mesoscopic scale simulations.

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Hao Wang

Papers

Random hopping among localized states and charge fluctuation at disordered surfaces

Atomic Simulations of the Interaction between a Dislocation Loop and Vacancy-Type Defects in Tungsten