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...

This research deals with a hybrid flow shop scheduling problem with parallel batching, machine eligibility, unrelated parallel machine, and different release dates to minimize the sum of the total weighted earliness and tardiness (ET) penalties. In parallel batching situation, it is supposed that number of machine in some stages are able to perform a certain number of jobs simultaneously. First...

This paper addresses a new mixed integer nonlinear and linear mathematical programming economic lot sizing and scheduling problem in distributed permutation flow shop problem with number of identical factories and machines. Different products must be distributed between the factories and then assignment of products to factories and sequencing of the products assigned to each factory has to be d...

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 ...

It is common belief that the Integrated Services architecture (IntServ) is not scalable to large networks as, e.g. the global Internet. This is due to the ambitious goal of providing per-flow QoS and the resulting complexity of finegrained traffic management. One solution to this problem is the aggregation of IntServ traffic flows in the core of the network. While one might suspect that aggrega...