OMA-Vol. 1 (2017), Issue 2, pp. 01–19 | Open Access Full-Text PDF

Abstract:The main theme of this work is to apply the Adomian decomposition method (ADM) to solve the non-linear differential equations which arise in fluid mechanics. we study some steady unidirectional magnetohydrodynamics (MHD) flow problems namely, Couette flow, Poiseuille flow and Generalized-Couette flow of a third grade non Newtonian fluid between two horizontal infinite parallel plates in the presence of a transversal magnetic field. Moreover, the MHD solutions for a Newtonian fluid, as well as those corresponding to a third grade fluid are obtained by the limiting cases of our solutions. Finally, the influence of the pertinent parameters on the velocity of fluids is also analyzed by graphical illustrations.

OMA-Vol. 1 (2017), Issue 1, pp. 44–59 | Open Access Full-Text PDF

Abstract: Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. It is experimentally proved that many properties of the chemical compounds and their topological indices are correlated. In this report, we compute closed form of forgotten polynomial and forgotten index for interconnection networks. Moreover we give graphs to see dependence of our results on the parameters of structures.

OMA-Vol. 1 (2017), Issue 1, pp. 34–43 | Open Access Full-Text PDF

Abstract:In this article, we are mainly interested to find some sufficient conditions for integral operator involving normalized Struve and Dini function to be in the class \(N\left( \mu \right)\). Some corollaries involving special functions are also the part of our investigations.

OMA-Vol. 1 (2017), Issue 1, pp. 25–33 | Open Access Full-Text PDF

Abstract: In this paper, we define a new generalized class of preinvex functions which includes harmonically \((s,m)\)-convex functions as a special case and establish a new identity. Using this identity, we introduce some new integral inequalities for harmonically \((s,m)\)-preinvex functions.

OMA-Vol. 1 (2017), Issue 1, pp. 13–24 | Open Access Full-Text PDF

Abstract: Let \(G\) be connected graph with vertex \(V(G)\) and edge set \(E(G)\). The first and second \(K\)-Banhatti indices of \(G\) are defined as \(B_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]\) and \(B_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]\) ,where \(ue\) means that the vertex \(u\) and edge \(e\) are incident in \(G\). The first and second \(K\)-hyper Banhatti indices of \(G\) are defined as \(HB_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]^{2}\) and \(HB_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]^{2}\). In this paper, we compute the first and second \(K\)-Banhatti and \(K\)-hyper Banhatti indices of Dominating David Derived networks.