Fractional matching preclusion for butterfly derived networks

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [18] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for butterfly network, augmented butterfly network and enhanced butterfly network

Investigation of material properties of yttria-stabilised zirconia using experimental techniques and first-principles calculations

Zirconia (ZrO2) exists in a monoclinic phase at ambient temperature and pressure. Increasing the temperature of zirconia brings about a transition from the monoclinic to a tetragonal phase, and then the formation of a cubic phase. Yttria (Y2O3) can be added to zirconia in order to stabilise the high temperature phases, resulting in forms of tetragonal and cubic zirconia that are stable at ambient temperature. These materials are ceramics and are known collectively as yttria-stabilised zirconia (YSZ). The primary aim of this thesis is to investigate the structural, electronic, vibrational and mechanical properties of zirconia in its three ambient pressure polymorphs, together with YSZ for a range of yttria concentrations. Firstly, short-range order is investigated by medium energy x-ray photoemission spectroscopy for a YSZ sample with 8-9 mol % Y2O3, in combination with first-principles density-functional theory (DFT) calculations for two YSZ structural models with 10.35 mol % Y2O3 and shows that both structural models have short-range order that agrees with results from XPS experiments. Secondly, long-range order is analysed by comparing results of neutron scattering experiments for crystals of the same yttria concentration, with the same two YSZ models. Comparison with calculated vibrational density of states for the two structural models indicates the occurrence of long-range order for one of the structures in agreement with the experimental result. Thirdly, these calculations are extended to a full study of the electronic partial density of states and vibrational density of states for ZrO2, and for YSZ models with 10.35, 14, 17, 20 and 40 mol % Y2O3. Lastly, mechanical properties are investigated through first-principles calculations of the bulk modulus, shear modulus, Young's modulus and Poisson's ratio for the three ambient-pressure phases of ZrO2 and compared to existing available experimental results. The ideal strength of cubic ZrO2 is calculated for strains in the [100], [110] and [111] directions and for YSZ with concentrations of 6.67 mol % and 14.29 mol % Y2O3 for strains in the [100] and [110] directions. The ideal strength is also calculated for YSZ with concentration of 6.67 mol % Y2O3 co-doped with titanium, manganese, calcium or nickel

Investigation of material properties of yttria-stabilised zirconia using experimental techniques and first-principles calculations

Zirconia (ZrO2) exists in a monoclinic phase at ambient temperature and pressure. Increasing the temperature of zirconia brings about a transition from the monoclinic to a tetragonal phase, and then the formation of a cubic phase. Yttria (Y2O3) can be added to zirconia in order to stabilise the high temperature phases, resulting in forms of tetragonal and cubic zirconia that are stable at ambient temperature. These materials are ceramics and are known collectively as yttria-stabilised zirconia (YSZ). The primary aim of this thesis is to investigate the structural, electronic, vibrational and mechanical properties of zirconia in its three ambient pressure polymorphs, together with YSZ for a range of yttria concentrations. Firstly, short-range order is investigated by medium energy x-ray photoemission spectroscopy for a YSZ sample with 8-9 mol % Y2O3, in combination with first-principles density-functional theory (DFT) calculations for two YSZ structural models with 10.35 mol % Y2O3 and shows that both structural models have short-range order that agrees with results from XPS experiments. Secondly, long-range order is analysed by comparing results of neutron scattering experiments for crystals of the same yttria concentration, with the same two YSZ models. Comparison with calculated vibrational density of states for the two structural models indicates the occurrence of long-range order for one of the structures in agreement with the experimental result. Thirdly, these calculations are extended to a full study of the electronic partial density of states and vibrational density of states for ZrO2, and for YSZ models with 10.35, 14, 17, 20 and 40 mol % Y2O3. Lastly, mechanical properties are investigated through first-principles calculations of the bulk modulus, shear modulus, Young's modulus and Poisson's ratio for the three ambient-pressure phases of ZrO2 and compared to existing available experimental results. The ideal strength of cubic ZrO2 is calculated for strains in the [100], [110] and [111] directions and for YSZ with concentrations of 6.67 mol % and 14.29 mol % Y2O3 for strains in the [100] and [110] directions. The ideal strength is also calculated for YSZ with concentration of 6.67 mol % Y2O3 co-doped with titanium, manganese, calcium or nickel

Fractional matching preclusion for generalized augmented cubes

The \emph{matching preclusion number} of a graph is the minimum number ofedges whose deletion results in a graph that has neither perfect matchings noralmost perfect matchings. As a generalization, Liu and Liu recently introducedthe concept of fractional matching preclusion number. The \emph{fractionalmatching preclusion number} of $G$ is the minimum number of edges whosedeletion leaves the resulting graph without a fractional perfect matching. The\emph{fractional strong matching preclusion number} of $G$ is the minimumnumber of vertices and edges whose deletion leaves the resulting graph withouta fractional perfect matching. In this paper, we obtain the fractional matchingpreclusion number and the fractional strong matching preclusion number forgeneralized augmented cubes. In addition, all the optimal fractional strongmatching preclusion sets of these graphs are categorized.Comment: 21 pages; 1 figure