A five-phase model for mathematical problem solving: Identifying synergies in pre-service-teachers’ metacognitive and cognitive actions

Based on empirical data from a study of pre-service teachers engaged in non-routine mathematics problem solving, a five-phase model is proposed to describe the range of cognitive and metacognitive approaches used. The five phases are engagement, transformation-formulation, implementation, evaluation and internalization, with each phase being described in terms of sub-categories. The model caters for a variety of pathways that can be adopted during any problem-solving process by recognizing that the path between these five phases is neither linear nor unidirectional.     

Interfacial properties of free-standing poly(3-hexylthiophene) films

Using full atomistic classical molecular dynamics simulations, the interfacial properties of free-standing poly(3-hexylthiophene) (P3HT) films have been investigated. The orientations of different parts of the P3HT chain and the surface tensions of the films were calculated in a temperature range of 540 K-600 K. At the liquid/vacuum interface, the P3HT chain shows ordering by exposing hexyl groups at the interface, while the chain backbone lays flat with the thiophene ring preferentially tilt toward the surface. At the interface, the terminal methyl groups of hexyl side chains are in excess compared to the methylene groups or thiophene rings. The surface tension of P3HT in its melt state shows similar temperature dependence to that of polymers that have long alkyl side chains. The surface tension values are comparable to those polymers that expose methyl or methylene groups on the surface. The surface tension values determined for the melt state are lower than the experimental reported values for crystalline P3HT films, as expected.     

Fuzzy scheduling of job orders in a two-stage flowshop with batch-processing machines

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.     

B,N-co-doped graphene-supported Ir and Pt clusters for methane activation and C─C coupling: A density functional theory study

Methane conversion by using transition metal catalysts plays in an important role in various usages of the industrial process. The mechanism of methane conversion on B, N-co-doped graphene supported Ir and Pt clusters, BNG-Ir4 and BNG-Pt4, have been investigated using density functional theory calculations. Methane was found to adsorb on BNG-Ir4 and BNG-Pt4 clusters via strong agostic interactions. The first step of methane dehydrogenation on BNG-Ir4 has a lower energy barrier, indicating a facile methane dissociation on BNG-Ir4. In addition, it shows that hydrogen molecule can form on the BNG-Ir4 and hydrogen can desorb from the surface. Besides, the C-C coupling reaction of CH₃ to form ethane is a more thermodynamically favorable process than CH₃ dehydrogenation on BNG-Ir4. Further, ethane is easier to desorb from the surface due to its low desorption energy. Therefore, the BNG-Ir4 cluster is a potential catalyst for activating methane to form ethane and to produce hydrogen. © 2019 Wiley Periodicals, Inc.     

Perfect Domination Polynomial of Homogeneous Caterpillar Graphs and of Full Binary Trees

Mathematical Notes - Let $$G=(V,E)$$ be a simple graph of order $$n$$ . A set $$S \subseteq V(G)$$ is a perfect dominating set of a graph $$G$$ if every vertex $$v\in V(G)-S$$ is adjacent to...