Denote by B∗ n the set of all k∗-cycle resonant hexagonal chains with n hexagons. For any Bn ∈ B ∗ n , let m(Bn) and i(Bn) be the numbers of matchings (=the Hosoya index) and the number of independent sets (=the Merrifield-Simmons index) of Bn, respectively. In this paper, we give a characterization of the k∗-cycle resonant hexagonal chains, and show that for any Bn ∈ B ∗ n , m(Hn) ≤ m(Bn) and ...

Abstract We report a “nano-on-micro” approach for growth of cactus-like nanostructures zinc oxide (ZnO) gas sensing application. use electrospun polymeric fibers doped with catalyst nanoparticles as the template and employ vapor-liquid-solid (VLS) method to ZnO nanostructures. Controlling processing variables in VLS process yields needle-like around fibers, which resembles needles cactus. The n...

Using atomistic molecular dynamic simulations we study the transitions between solid herringbone and liquid crystalline hexagonal mesophases of discotic liquid crystals formed by hexabenzocoronene derivatives. Combining a united atom representation for the side chains with the fully atomistic description of the core, we study the effect of side chain substitution on the transition temperatures ...

Using density functional theory and generalized gradient approximation for exchange and correlation, we present theoretical analysis of the electronic structure of recently synthesized graphyne and its boron nitride analog (labeled as BN-yne). The former is composed of hexagonal carbon rings joined by C-chains, while the latter is composed of hexagonal BN rings joined by C-chains. We have explo...

Let T be an edge weighted tree, let dT (u, v) be the sum of the weights of the edges on the path from u to v in T , and let dmin and dmax be two non-negative real numbers such that dmin ≤ dmax. Then a pairwise compatibility graph of T for dmin and dmax is a graph G = (V, E), where each vertex u ∈ V corresponds to a leaf u of T and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dm...

Ecological speciation occurs with the adaptation of populations to different environments and concurrent evolution of reproductive isolation. Phenotypic plasticity might influence both ecological adaptation and reproductive traits. We examined environment-specific gene expression and male mating success in cactophilic Drosophila mojavensis using transcriptome sequencing. This species exhibits c...

Broadcasting is the process of dissemination of a message from one vertex (called originator) to all other vertices in the graph. This task is accomplished by placing a sequence of calls between neighboring vertices, where one call requires one unit of time and each call involves exactly two vertices. Each vertex can participate in one call per one unit of time. Determination of the broadcast t...