On additive functions having a non-decreasing normal order

On the Normal Order of Arithmetic Functions.

On construction of non-normal Boolean functions

Given two non-weakly k-normal Boolean functions on n variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)variables.

Normal edge-transitive Cayley graphs on the non-abelian groups of order $4p^2$, where $p$ is a prime number

In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.

Additive Functions on Shifted Primes

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes. A real-valued function / defined on the positive integers is additive if it satisfies f(rs) = f(r) + f(s) whenever r and s are coprime. Such functions are determined by their values on the prime-powers. For additive arithmetic function /, let Q denote the frequency...

On Certain Large Additive Functions

pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...