Decision problems in the space of Dehn fillings

Normal surface theory is used to study Dehn fillings of a knot-manifold. We use that any triangulation of a knot-manifold may be modified to a triangulation having just one vertex in the boundary. In this situation, it is shown that there is a finite computable set of slopes on the boundary of the knot-manifold, which come from boundary slopes of normal or almost normal surfaces. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely those manifolds obtained by Dehn filling of a given knot-manifold that: (1) are reducible, (2) contain two-sided incompressible surfaces, (3) are Haken, (4) fiber over S¹, (5) are the 3-sphere, and (6) are a lens space. Each of these algorithms is a finite computation.Moreover, in the case of essential surfaces, we show that the topology of each filled manifold is strongly reflected in the combinatorial properties of a triangulation of the knot-manifold with just one vertex in the boundary. If a filled manifold contains an essential surface then the knot-manifold contains an essential normal vertex solution which caps off to an essential surface of the same type in the filled manifold. (Normal vertex solutions are the premier class of normal surface and are computable.)     

\mathbb Z _2-Thurston norm and complexity of 3-manifolds

A new lower bound on the complexity of a 3-manifold is given using the ${\mathbb Z }_2$ -Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of quadrilateral discs.     

Synthesis of Polypeptide Block Copolymer Hybrids by the Combination of N‐Carboxyanhydride Polymerization and RAFT

The synthesis of hybrid bioconjugates via the ring‐opening polymerization (ROP) of N‐carboxyanhydrides (NCAs) using a synthetic macroinitiator is described. Poly(n‐butyl acrylate), polystyrene, and poly(N‐isopropyl acrylamide) are synthesized (polydisperity index, Đ < 1.1) using reversible addition–fragmentation chain transfer (RAFT) as the synthetic tool. A phthalimidomethyl trithiocarbonate RAFT chain transfer agent is used to prepare well‐defined, end‐functional polymers, which after deprotection result in amine terminal macroinitiators. The subsequent initiating systems could successfully be chain extended with ε‐benzyloxycarbonyl‐l ‐lysine or γ‐benzyl‐l ‐glutamate as the NCAs to produce a library of polymer–polypeptide conjugates. In doing so, a novel procedure for directly synthesizing bioconjugates via a non‐modular route without the need for excessive purification and isolation steps is described.

     

Fast- and ultra-fast laser pulse induced reactions between carbon dioxide and methane

The direct excitation of CO_2 using fast (nanosecond) and ultrafast (femtosecond) pulsed lasers was investigated. A gas reaction cell was used to excite CO_2 in a 50:50 mixture of CO_2 and CH_4 using nano- and femtosecond laser systems, to induce a reaction between these two compounds. FT-IR spectra showed that CO was formed using the nanosecond and femtosecond laser systems. It was also found that hydrocarbons, containing C-C bonds were formed. For both the nanosecond and femtosecond laser, it was found that more C-C higher hydrocarbons were formed after 5 h compared to 3 h of irradiation. Irradiation at pressures of 250, 350 and 500 kPa with the femtosecond laser system showed the expected increase in the amount of CO formed with an increase in pressure. Results from this study showed that carbon dioxide and methane can be activated successfully using nanosecond laser pulses at 2000 run and femtosecond laser pulses at 795 or 2000 nm and that these activated species react to form CO and C-C containing products.     

Direct crystallisation of a hydroxy sodalite membrane without seeding using a conventional oven

A double layered hydroxy sodalite membrane was synthesised directly onto a tubular -alumina support without seeding using a conventional hot-air oven. The effect of different synthesis parameters including the water content, ageing period, synthesis time and temperature, on the purity and continuity of the membrane was investigated. The water content was an important factor in controlling the presence of contaminating zeolite phases in the membrane. The optimised membrane which was contaminant free was characterised by XRD, SEM and single gas permeation using He, N₂ and SF₆. The permeance of the three gases through the membrane ranged from 0.8 to 8 × 10⁻⁸ mol m⁻² s⁻¹ Pa⁻¹. The selectivity ( = 2.5–2.7) compared well to the Knudsen diffusion ratio for He/N₂.     

Single gas permeation through compositionally different zeolite NaA membranes: Observations on the intercrystalline porosity in an unconventional,semicrystalline layer

The successful application of zeolite A membranes in the industrial market has thus far been restricted to the pervaporative dehydration of solvent streams in the pharmaceutical and engineering industries. Their application in gas separation processes remains elusive, largely due to the existence of uncontrollable, intercrystalline diffusion pathways in the boundary regions of neighbouring crystals.     

Multipolymers with Fischer-Tropsch olefins

Multipolymers consisting of ethylene, 1-heptene, 3-methylpentene and 4-methylpentene were prepared with a heterogeneous Ziegler-Natta catalyst. The polymers were prepared in such a way that the molar fraction of the comonomers remained the same. Copolymers of ethylene/1-heptene and ethylene/4-methylpentene were prepared in order to study the changes in polymer characteristics as one moves from an ethylene/linear alpha olefin copolymer through ethylene multipolymers to an ethylene/4-methylpentene copolymer. The mechanical, rheological and application properties showed expected trends.     

Synthesis, complete 1H and 13C NMR assignment and crystal structure of novel epoxide derivatives of cytochalasin B

Five novel epoxide derivatives of cytochalasin B were synthesized. Reaction of cytochalasin B with t-BHP and BuLi led to selective epoxidation of the C-21/22 double bond to give a single monoepoxide, while reaction with m-CPBA yielded two diepoxides. Reaction of the monoepoxide with m-CPBA yielded two triepoxides. The relative configurations of the epoxides were elucidated by analogy with the natural product by means of spectroscopic methods; full assignment of NMR signals was achieved, and the absolute configuration was confirmed by X-ray crystallography.