Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

Photooxidation of Selected Polycyclic Aromatic Hydrocarbons in Aqueous Organic Media in The Presence of Ti(IV)Oxide

Abstract

We have studied the photooxidation of selected polycyclic aromatic hydrocarbons (PAH) in the presence of Ti(IV)oxide in a mixed solvent system consisting of N-methylpyrrolidinone (NMP) and water. Reaction rates for the photooxidation of acenaphthylene and pyrene were investigated by monitoring the disappearance of the PAH substrate from the reaction mixture as a function of time. For both compounds plots of In C_o/C_t, as a function of time yielded straight lines, indicating first order kinetics with respect to the substrate. With an initial acenaphthylene concentration of 1.0 gL^?1 the first order reaction rate constant was 0.19 hr^?1 and the half life was 3.7 hr. With an initial pyrene concentration of 0.2 gL^?1 the first order reaction rate constant was 0.0285 hr^?1 and the half life was 24 hr. The photoproducts were characterized by high performance liquid chromatography with diode-array detection (HPLC/DAD) and by liquid chromatography/atmospheric pressure chemical ionization mass spectrometry (APCI/LC-MS). Although a number of simple oxidation products were identified the bulk of the photoproducts consisted of the parent PAH substituted with one or more solvent (NMP) molecules. The product mixtures from the photooxidation of the non-mutagens acenaphthylene and pyrene were found to be also non-mutagenic in our Salmonella typhimurium forward mutation assay.     

Polyesters by a Radical Pathway: Rationalization of the Cyclic Ketene Acetal Efficiency

Radical ring-opening polymerization (rROP) of cyclic ketene acetals (CKAs) combines the advantages of both ring-opening polymerization and radical polymerization thereby allowing the robust production of polyesters coupled with the mild polymerization conditions of a radical process. rROP was recently rejuvenated by the possibility to copolymerize CKAs with classic vinyl monomers leading to the insertion of cleavable functionality into a vinyl-based copolymer backbone and thus imparting (bio)degradability. Such materials are suitable for a large scope of applications, particularly within the biomedical field. The competition between the ring-opening and ring-retaining propagation routes is a major complication in the development of efficient CKA monomers, ultimately leading to the use of only four monomers that are known to completely ring-open under all experimental conditions. In this article we investigate the radical ring-opening polymerization of model CKA monomers and demonstrate by the combination of DFT calculations and kinetic modeling using PREDICI software that we are now able to predict in silico the ring-opening ability of CKA monomers.     

On certain spanning subgraphs of embeddings with applications to domination

We prove the existence of certain spanning subgraphs of graphs embedded in the torus and the Klein bottle. Matheson and Tarjan proved that a triangulated disc with n vertices can be dominated by a set of no more than n/3 of its vertices and thus, so can any finite graph which triangulates the plane. We use our existence theorems to prove results closely allied to those of Matheson and Tarjan, but for the torus and the Klein bottle.     

Accelerated ageing and degradation in poly-l-lactide/hydroxyapatite nanocomposites

Dry, compression molded films of medical grade poly-l-lactide (PLLA) showed a marked reduction in tensile strength and strain after accelerated ageing in aqueous NaOH at 50 °C, accompanied by mass loss, surface erosion, increased hydrophilicity and, in the case of the initially amorphous films, cold crystallization owing to the plasticizing effect of the ageing medium. Addition of well dispersed nanosized hydroxyapatite (nHA) particles resulted in increases in the rate of mass loss during ageing, identified with accelerated degradation at the matrix/particle interfaces. However, the associated decreases in tensile strength and strain to fail with ageing time were far less marked in the presence of the nHA than in the unmodified films. This implied that nHA acts as an effective toughener of the bulk material, consistent with TEM observations of the deformed films, which indicated failure of the particle-matrix interfaces to promote plastic deformation of the PLLA.     

Morphological investigation of polylactide/microfibrillated cellulose composites

Optical microscopy and transmission electron microscopy have been used to investigate the morphology of polylactide (PLA)/microfibrillated cellulose (MFC) composites prepared by: compression molding of wet-comingled MFC and PLA latex or powder, twin-screw extrusion of the wet-comingled compounds, and solvent mixing of PLA with MFC or acetylated MFC. Compression molding of wet-comingled MFC and PLA latex or powder compounds resulted in a cellular MFC network, whereas solvent-cast films showed a more uniform dispersion of MFC fibers. Somewhat lower aggregate diameters observed in the acetylated MFC were assumed to be due to decreased MFC hydrophilicity and improved chemical affinity with the PLA matrix. The MFC networks in the commingled compounds were severely disrupted after twin-screw extrusion. This confirmed the limited deformability of the networks inferred from the extensive syneresis during the initial compression molding step, and accounted for substantial losses in stiffness reinforcement by the MFC after extrusion.     

Elastic properties of some bulk metallic glasses

The relationships between the elastic moduli, glass forming ability and response to deformation of bulk metallic glasses are investigated. Five bulk metallic glasses are prepared from high purity elements via suction casting. The results confirm that there exists a correlation between energy absorbed to failure during compression testing and the bulk to shear modulus ratio. This finding is developed such that it corresponds only to the elastic component of energy absorption, and that the bulk modulus dominates this. Plastic deformation appears to be favored by a reduced shear modulus, although it shows greater dependence on structural features that are frozen in during the glass transition, and so may well be dependent on the liquid fragility.     

Frequency modelling and solution of fluid–structure interaction in complex pipelines

Complex pipelines may have various structural supports and boundary conditions, as well as branches. To analyse the vibrational characteristics of piping systems, frequency modelling and solution methods considering complex constraints are developed here. A fourteen-equation model and Transfer Matrix Method (TMM) are employed to describe Fluid–Structure Interaction (FSI) in liquid-filled pipes. A general solution for the multi-branch pipe is proposed in this paper, offering a methodology to predict frequency responses of the complex piping system. Some branched pipe systems are built for the purpose of validation, indicating good agreement with calculated results.