: We investigate the electronic and transport properties of circular graphene structures (quantum dots) that include a pentagonal defect. In our calculations, we employ a tight-binding model determining total and local density of states, transmission function and participation number. For the closed structure, we observe that the effect of the defect is concentrated mainly on energies near to z...

The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. uncertain information characterized by Pentagonal fuzzy numbers. To solve the problem, in paper, two different strategies are proposed; one relies on idea ranking function, and other close interval approximation pentagonal number. For persons that need be more speci...

the wiener index is the sum of distances between all pairs of vertices in a connected graph. in this paper, explicit expressions for the expected value of the wiener index of three types of random pentagonal chains (cf. figure 1) are obtained.

Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

In this paper, medical diagnosis concerning isolated systolic hypertension and a study on implication operators is introduced, but fuzzy pentagonal number matrix concepts developed to give numerical example graphical representation are also established.

In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler’s pentagonal number theorem, Ramanujan’s for finding the relations.