For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [...

The dilations {aj} are lacunary, for example aj = 2 , and the coefficients cj,k are explicit local averages of f , or even pointwise sampled values, when f has some smoothness. For convergence just in W m−1,p(Rd) the scale averaging is unnecessary and one has the simpler formula f(x) = limj→∞ P k∈Zd cj,kψ(ajx − k). The Strang–Fix rates of approximation are recovered. As a corollary of the scale...

The reactions of [γ-SiW10O36](8-) represent one of the most important synthetic gateways into a vast array of polyoxotungstate chemistry. Herein, we set about exploring the transformation of the lacunary polyoxoanion [β2-SiW11O39](8-) into [γ-SiW10O36](8-) using high-resolution electrospray mass spectrometry, density functional theory, and molecular dynamics. We show that the reaction proceeds ...

In this paper, we extend an inequality concerning the polar derivative of a polynomial in Lp-norm to class lacunary polynomials and thereby obtain bound that depends on some coefficients as well.

We prove the sharp weighted-L2 bounds for strong-sparse operators introduced in [3]. The main contribution of paper is construction a weight that lacunary mixture dual power weights. This helps to sharpness trivial upper bound operator norm.

Abstract The reduction modulo p of a family lacunary integer polynomials, associated with the dynamical zeta function ζ β ( z )of -shift, for β> 1 close to one, is investigated. We briefly recall how this correlated problem Lehmer. A variety questions raised about their numbers zeroes in

The purpose of this paper is to introduce the concepts of lacunary almost statistical convergence and strongly almost convergence of generalized difference sequences of fuzzy numbers. We obtain some results related to these concepts. It is also shown that lacunary almost statistical convergence and strongly almost convergence are equivalent for bounded sequences of fuzzy numbers. θ m Δ θ m Δ m ...

A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...