Abstract:Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

Abstract:Let \(S\) be a dominating set of a graph \(G\). The set \(S\) is called a pendant dominating set of \(G\) if the induced subgraph of \(S\) contains a minimum of one node of degree one. The minimum cardinality of the pendant dominating set in \(G\) is referred to as the pendant domination number of \(G\), indicated by \(\gamma_{pe}(G)\). This article analyzes the effect of \(\gamma_{pe}(G)\) when an arbitrary node or edge is removed.

Abstract:In this paper, we have proposed new windmill graph, that is Basava wheel windmill graph. The Basava wheel windmill graph \(W^{(m)}_{n+1}\) is the graph obtained by taking \(m\geq 2\) copies of the graph \(K_1+W_{n}\) for \(n\geq 4\) with a vertex \(K_1\) in common. Inspired by recent work on topological indices, proposed new degree-based topological indices namely, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of a graph \(G\). We have obtained first and second Zagreb index, F-index, first and second hyper-Zagreb index, harmonic index, Randi\(\acute{c}\) index, general Randi\(\acute{c}\) index, sum connectivity index, general sum connectivity index, atom-bond connectivity index, geometric-arithmetic index, Symmetric division deg index, Sombor index, SK indices, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of Basava wheel windmill graph. Further, we have computed exact values of these topological indices of chloroquine, hydroxychloroquine and remdesiver.

Abstract:Our primary purpose is to compute explicitly traces of the Dirichlet forms related to Feller’s one-dimensional diffusions on countable sets via Fukushima’s method. For discrete measures, the obtained trace form can be described as a Dirichlet form on the graph.

Abstract:In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}x^{k}W_{mk+j}^{3}\) for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.