Integral transform is one of the techniques in function transformation methods. transforms have been interesting tools for solving different problems arising applied mathematics, mathematical physics and engineering science at least two centuries. We studied an extended fractional Mellin generalized sense. For this testing space E its dual E* are considered. investigated inversion formula by us...

This paper provides a lexical entry schema for exclusives covering the adverbs only, just, exclusively, merely, purely, solely, simply, and the adjectives only, sole, pure, exclusive and alone. We argue, on the basis of inter-paraphrasability relations among these exclusives and entailments involving at least and at most, that all of these items make an at-issue contribution of an upper bound o...

Abstract: We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical probability approach, Stein’s method, an analytic approach and a new approach based on Krawtchouk polynomials and the Parseval identity. We also exte...