We give a reduction formula for the Waring number g(k, q) over finite field $$\mathbb {F}_q$$ . By exploiting relation between with diameter of generalized Paley graph $$\Gamma (k,q)$$ and by using characterization due to Pearce Praeger (2019) those which are Cartesian decomposable, we obtain $$\begin{aligned} g(\tfrac{p^{ab}-1}{bc},p^{ab}) = b g(\tfrac{p^a-1}{c},p^a) \end{aligned}$$ p prime a,...

In this paper, we give a generalized Cline?s formula for the Drazin inverse. Let R be ring, and let a, b, c, d ? satisfying (ac)2 = (db)(ac), (db)2 (ac)(db), b(ac)a b(db)a, c(ac)d c(db)d. Then ac Rd if only bd Rd. case, (bd)d b((ac)d)2d: We also present formulas group inverses. Some weaker conditions in Banach algebra are investigated. These extend main results of on g-Drazin inverse Liao, Chen...

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certai...