Abstract We consider two recent conjectures made by Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index exclusive number of graphs. One conjecture posits an exact relationship first invariants; we show that in fact predicted value may be arbitrarily far from truth either direction. In process establish some new bounds on both...

co-channel interference is a major factor in limiting the capacity and link quality in cellular communications. as the co-channel interference is modeled by lognormal distribution, sum of the co-channel interferences of neighboring cells is represented by the sum of lognormal random variables (rvs) which has no closed-form expression. assuming independent, identically distributed (iid) rvs, the...

We solve Diophantine equations of the type $ \, a (x^3 + y^3 z^3 ) = (x y z)^3$, where $x,y,z$ are integer variables, and coefficient $a \neq 0$ is rational. show that there infinite families such equations, including those $a$ any ratio cubes or certain rational fractions, have nontrivial solutions. There also do not solution, $1/a 1 - 24/m$ with restrictions on $m$. The can be represented by ...

In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.