We offer some new identities for a bipartition function, which has a relation to a Hecke-type identity of Andrews. Further, we show this partition function is lacunary, and relate it to a real quadratic field.

The idea of difference sequences was first introduced by Kizmaz [4]. In this first paper we define some generalized difference sequence combining lacunary sequences and Orlicz function. We establish some relations between these sequence space.

We find asymptotics for lacunary sums of binomial coefficients. As an application we determine the exact and approximate probability that the first card has the uniquely highest rank among the top l cards of a standard card deck.

Transition-metal substituted Keggin-type polyoxometalates (POMs) are of great interest for applications in biomedicine, material science and catalysis. The synthesis transition metal-substituted polytungstates via the formation a lacunary...