In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

In this paper, we study the Lehmer’s type congruences for lacunary harmonic sums.

We consider the lacunary Dirichlet series obtained by taking the reciprocals of the s-th powers of the Fibonacci numbers. This series admits an analytic continuation to the entire complex plane. Its special values at integral arguments are then studied. If the argument is a negative integer, the value is algebraic. If the argument is a positive even integer, the value is transcendental by Neste...

We study the nodal set of Laplace eigenfunctions on flat 2d torus $${\mathbb {T}}^2$$ . prove an asymptotic law for length such eigenfunctions, under some growth assumptions their Fourier coefficients. Moreover, we show that is asymptotically equidistributed The proofs are based Bourgain’s de-randomisation technique and main new ingredient, which might be independent interest, integrability arb...

Lacunary polyoxometalates (POMs) are negatively charged metal–oxo clusters, formally obtained from plenary topologies via fragment removal. Owing to the removal, lacunary POMs archetypes rich in nucleophilic terminal oxo ligands, making them suitable for post-synthetic coordination with various heterometals. Trilacunary heteropolytungstates (hetero-POTs) based on bowl-shaped {W9O30} framework i...

Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

In this paper we study the concept of lacunary statistical convergent triple sequences in probabilistic normed spaces and prove some basic properties.