In this thesis we shall consider two topics that are contained in combinatorial group theory and concern properties of finitely presented groups. The first problem we examine is that of calculating the Fibonacci length of certain families of finitely presented groups. In pursuing this we come across ideas and unsolved problems from number theory. We mainly concentrate on finding the Fibonacci length of powers of dihedral groups, certain Fibonacci groups and a family of metacyclic groups. The second problem we investigate in this thesis is finding if the group PGL(2, p), for p a prime, is efficient on a minimal generating set. We find various presentations that define PGL(2,p) or C2 x PSL(2,p) and direct products of these groups. As in the previous sections we come across number theoretic problems. We also have occasion to use results from tensor theory and homological algebra in order to obtain our results.

This thesis is concerned with a topic in combinatorial group theory and, in particular, with a study of some groups with finite presentations. After preliminary definitions and theorems we describe the Todd-Coxeter coset enumeration algorithm and the modified Todd-Coxeter algorithm which shows that, given a finitely generated subgroup H of finite index in a finitely presented group G, we can find a presentation for H. We then give elementary examples illustrating the algorithms and include a discussion on the computer programmes that are to be used. In the main part of the thesis we investigate two classes of cyclically presented groups. Supposewhere w1 = w is a word in a1,a2,...,an, and wi+1 is obtained from wi by applying the permutation (1 2 ... n) to the suffices of the a's. The first class we investigate are the groups that is the groups G(l,m,n) are groups of type G2 (w). Secondly we investigate the Fibonacci-type groups H(r,n,k,s,h) obtained when, for some integers r,s,h > 1, k > O, the word w is given by Fibonacci groups being the special case given by k = s = h = 1. For both classes we begin by giving some homomorphisms and isomorphisms that may be obtained. We show, using the Todd-Coxeter algorithm when appropriate, that the six groups G(2,2,3), G(2,2,-3), G(-l,-l,4), G(2,3,-2), G(-2,2,-1) and G(-2,3,l) are finite non-metacyclic groups of deficiency zero, having orders 215.33, 28.33, 29.3.5, 23.33.7, 23.3.5.11 amd 23.36 respectively. We also show that the groups G(1-n, 6, n) where n = 1 mod 5 give an infinite series of non-metacyclic groups. We consider the structure of the non-metacyclic groups H(3,6,1,1,1) and H(3,6,5,l,2) both of order 1512, showing that neither is isomorphic to G(2, 3, -2) another non-metacyclic group of order 1512. In a paper on the Fibonacci groups D.L. Johnson, J.W. Wamsley and D. Wright pose two questions relating to the Fibonacci groups for the case r = 1 mod n, namely to find 2-generator 2-relation presentations for them and also their orders. We answer these questions and generalise the results to the class H(r,n,k,s,1) where it is shown that H(r,n,k,s,1) is metacyclic if (i) r = s mod n, (ii) (r,n) = 1, (iii) (r + k - 1, n) - 1, and a 2-generator 2-relation presentation is found for these groups. Further if (iv) (r,s) = 1, then we show that H(r,n,k,s,1) is a finite metacyclic group of order rn - sn. A possible generalisation to the groups H(r,n,k,s,h) is considered. Finally the metacyclic groups H(r,4,1,2,1), r odd are discussed.

The study of the following compounds is based on the premise that high symmetry in molecules should lead to low barriers to molecular motion even in the solid state i.e. the principle of least distress. The study of 3,3-diethylpentane is a very nice example of a phase change which results in no chemical shift changes but, produces a sharp discontinuity in the rate of ethyl group rotation. A large discontinuity in rate of molecular motion is also observed in 4,4-dipropylheptane which is also due to a phase change. The following study of tetraalkyl ammonium halides revealed both alkyl group rotation and cation tumbling to be occurring. This is most significant in the tetramethyl ammonium halides where the effects of methyl rotation and cation tumbling are shown to overlap considerably. The activation energies for the cation tumbling in the tetramethyl ammonium halides are Ea= 30 - 36 kJ mol−1 and for ethyl group rotation in tetraethyl ammonium chloride are, △H†; = 57.8 kJ mol−1 and △S†; = 45.9 J K−1 mol−1. The chemical shift differences in each chain due to different chain lengths is seen in tetrabutyl ammonium iodate which also shows a sudden coalescence and introduction of rapid molecular motion after two small phase changes. This compound has a large phase change which also affects the rate of molecular motion. The tetraalkyl phosphonium halides have a greater degree of molecular motion than the ammoniums in the temperature range studied and also offer the chance to use Tip measurements. The tetramethyl phosphonium halides show a distinct cation tumbling as opposed to the ammoniums. The process in the chloride and bromide which have hexagonal structures gives △H†; ~ 30 kJ mol−1 and negative △S†; values and the lower symmetry iodide has △H†; = 45.2 kJ mol−1 and a positive value of △S†;. The tetraethyl phosphonium halides show ethyl group rotations measurable to varying degrees by 13CT1p. The tetrabutyl phosphonium halides also have the different chain lengths as seen for the ammonium compounds. They also show bond rotations which are quite difficult to measure by 13CT1p values. The study of bis-(hydroxymethyl)cyclopentane (BHMCP) in an attempt to study ring puckering/pseudorotation in cyclopentane derivatives in the solid state reveals a hydrogen bond exchange process (△Gc†;~ 60 kJ mol−1). The bicyclic derivatives of BHMCP showed no such molecular motions but did reveal some interesting solid- solid phase transitions and chemical shift changes. The study of trans-cyclopentanediol yields △H†; = 77.0 and △S&†; = 184 J K−1 mol−1 for the processes involved. The study of 4,4-dimethyl-trans−1,2-cyclopentanediol reveals two processes. One results in the coalescence of resonances and appears to be a hydrogen bonding exchange process. The other is a much lower energy process (Ea ~ 26 kJ mol−1) which could be a ring puckering process. The study of sulpholane also shows significant molecular motion with △H&†; = 50.6 kJ mol−1 and △S&†; = 77.9 J K−1 mol−1.

Cell proliferation kinetics of plasmacytoma has been assessed in vitro and in vivo. The proliferation of plasmacytoma and other cell cultures in vitro has been assessed in terms of the culture environment, and humoral mediators (UIF) produced by cells of the central and peripheral lymphoid tissues. Foetal calf serum (FCS), has been demonstrated to influence DNA synthesis as assessed in terms of isotope uptake by cell cultures. The amount of radioactivity in the acid soluble and insoluble pools, was reduced as the concentration of FCS in the culture was increased. The relative change in isotope availability in both pools was approximately similar. The reduction of isotope activity in the acid soluble pool may suggest that FCS was interfering with the transport of isotope across the cell membrane; and the reduction of isotope activity in the acid insoluble pool may be a consequence to the effects observed in the acid soluble pool. The inhibition of isotope uptake by FCS may depend on several factors, such as, the batch of FCS, the type of cell culture under investigation, its culture density, culture incubation time and culture incubation sequence. FCS may interact with other substances available in the culture environment, either by increasing or decreasing the relative amount of isotope uptake by the respective cultures. The uptake of isotope by cell cultures that secrete polyamines into their culture environment which contains FCS, will consequently be reduced. The inhibitory effects of some UIF preparations on the uptake of isotope by cell cultures were modulated by FCS, and by the culture incubation sequence. The inhibitory effects of some of the fractions of UIF at some incubation sequences (with FCS), may be regarded as either "false positives" or the inhibition is a transitional one in the sense that it depended on the incubation sequence. Thus the interpretation in the change of radioisotope uptake must be viewed critically. UIF may contain heat sensitive substances, as the inhibitory effect of UIF 56c remained stable in both FCS environments and this may suggest that some factors in UIF which were heat sensitive were reacting with FCS to influence the inhibitory pattern of radioisotope uptake. Similarly the inhibitory effects of polyamines without FCS on the uptake of isotope by cell cultures, were evident when the culture incubation sequence was changed. Supernatants (UIF) produced by cells from the spleen, lymph nodes, bone marrow and thymus, were found to inhibit the uptake of isotope by cell cultures. The UIFS, which were obtained from the spleen, have demonstrated that the macrophage was the main source for the production of the inhibitory supernatants. The inhibitory material may contain a variety of substances, apart from thymidine, which may contribute to the regulation of cell proliferation. The growth kinetics of plasmacytoma in vivo, in two different immunological environments have revealed that tumour growth may also be controlled in T-cell deficient environments, as the latency period of tumour growth, was longer in the "nude" mice than in the normal counterparts Balb/c mice. Natural killer cells and macrophages may be some of the contributors to the suppression of tumour cell proliferation in the earlier periods of tumour growth. The growth kinetic studies of plasmacytoma in vivo, have demonstrated that the tumour birth rate was decreasing with increasing tumour age. Cell loss was approximately similar at the different stages of tumour growth, thus the growth fraction and the average intermitotic time may be influencing the cell production rate. The birth rate was assessed in terms of a weighted and unweighted least square regressions, to compare the reductions in error variability associated with the metaphase "Collection Function" curves, and its consequent effects on the standard errors of the respective Tea associated with each birth rate curve. In some birth rate curves the variance was generally proportional to the metaphase index, but in others the variance was not proportional. To reduce the error variability associated with the birth rate curves, other types of transforms may be required apart from the variance weighted transform.

The measurement of photosynthesis of submerged aquatic macrophytes was investigated with particular reference to water movement over a leaf surface. Light and dark 14C incorporation rates of two broadleaved pondweeks, Potamogeton perfoliatus and P. praelongus, were measured in the laboratory using procedures developed for use during in situ field productivity estimates. These measurements are used to evaluate the errors involved in the estimation of photosynthesis rates by this method and to provide recommendations for reducing these errors. Large variations in the 14C uptake, of replicate leaves or cut discs, were correlated with the position of the leaf on the stem and with the position of the disc on the leaf. Variation due to the size of the disc and to the effect of cutting were much less pronounced. Measurement of the rate of release of previously incorporated 14C from leaves showed that the release of carbon dioxide is greater in the dark than in the light, suggesting that extensive refixation is occurring and that this method will overestimate net photosynthesis and underestimate gross photosynthesis in light/dark bottle experiments. The movement of 14CO2 from the roots to the leaves of a plant was shown to be small and it is concluded that this may be disregarded as a significant source of carbon dioxide for photosynthesis. The ratio of leaf area to fluid volume in experimental enclosures was shown to correlate with the size of the pH changes caused by photosynthesis. Changes in pH occurring during typical in situ experiments were shown to be significantly larger than those occurring naturally and it is recommended that large enclosures with small quantities of leaf tissue are used. Reynolds number calculations shown that laminar boundary layers might be expected to predominate for broad leaves in both the aquatic and terrestrial situation. Theoretical boundary layer thicknesses, for leaves of similar sizes at similar bulk fluid velocities, show that the laminar boundary layer in water will be approximately four times less than that in air. Turbulent flow produced increases of more than 40% in measured 14C incorporation over unstirred enclosures. Different laminar flow rates over the surface of leaf discs produced measurable changes in the rate of 14C incorporation, showing a correlation between laminar boundary layer thickness and the rate of 14CO2 uptake. These measurements show that the diffusion of free carbon dioxide across the average laminar boundary layer would not be fast enough to support the flux of 14C, which must be assisted by the diffusion of the bicarbonate ion.

Although relative ground based stellar photometry has been an established investigative technique for many years, there have been very few programmes which have provided absolute stellar fluxes and indeed where such results have been published, they have been derived mainly from spectro-photometric data for a few bright stars. Such measurements are essential for the confirmation of model atmosphere calculations and for those models relating to early type stars, it is essential to extend such observations well into what is known as the vacuum ultraviolet region, i.e. below 3000A. The measurements are technically very difficult because of the need to use balloon or rocket platforms and when this work was started in 1962, only a very few observations had been conducted by the Naval Research Laboratory in Washington using very simple photometers with no absolute calibration. Under the auspices of a Senior Research Fellowship (the first in Scotland), held at the Royal Observatory, Edinburgh, the author proposed to the newly formed European Space Research Organisation, a number of stellar investigations aimed at obtaining absolute stellar fluxes in the region 1200Å - 2800Å. This thesis gives an account of almost a decade spent in developing the techniques of rocket astronomy and absolute calibration in the vacuum ultraviolet. Since no other European groups were engaged in similar studies, it was necessary for the author to essentially begin at the very beginning and a substantial period was spent in designing and testing optical systems which would withstand a typical Skylark Rocket launch. Systems of this type had never been flown before and many hours of vibration testing were necessary to ensure a satisfactory optical and mechanical configuration. The choice of a suitable ultraviolet detector was not easy and a substantial part of the early laboratory research was aimed at evaluating commercially available detectors and in the end an entirely new range of photo-multipliers was developed as a co-operative venture between the author and E.M.I. Hayes, Middlesex, resulting in a commercially saleable product. Wavelength isolation techniques were developed and the use of reflective mirror surfaces was successfully pioneered. A complete range of rocket-borne electronic systems was developed including solid state electrometers and high voltage power supplies. The techniques for encapsulating photomultipliers to withstand the rocket environment and the mounting of large optical mirrors were successfully developed and over fifty telescopes constructed and launched. The problems of calibrating on an absolute basis these rocket borne telescopes of large aperture were investigated and a network of traceable sub-standards was developed which ensured comparison with other (American) data. Highly stable microwave sources were developed and detectors calibrated at several national laboratories. These techniques were eventually used in the calibration of the T.D.I. S2/68 satellite experiment. The problem of integration of the payloads at centres throughout Europe was successfully overcome and the development of range facilities undertaken. Seven fully instrumented Skylarks were proposed and launched with a total of twenty photometers out of fifty-five photometers actually observing the Sky. The remainder having failed to produce any data due to rocket failure. During the period of the investigation, i.e. (1962-1970) the author obtained the first absolute stellar fluxes above the Earth's atmosphere and the total observations obtained equalled that obtained by all the other U.S. Groups including the satellite results of A. Smith. The results were compared with current model atmosphere calculations and showed that if blanketed models were used, the results would be to within ±0.25 magnitude in the region 1400Å-2800Å. The results also showed that it was possible to establish an absolute calibration network which was capable of not only permitting inter-comparison between the author's photometers, but also with other rocket groups, a situation that had hitherto been impossible. These results were the only stellar data to be obtained by any Group within the ESRO rocket programme. No other European results were obtained during that period.

Amyloglucosidase has been obtained from Rhizopus delemar and purified by ammonium sulphate fractionation; ethanolic precipitation; chromatography on DEAE-cellulose, DEAE-sephadex A-50 and Sephadex G-50/ Amberlite IRC-50. Ethanolic precipation and chromatography on DEAE-cellulose by stepwise elution have been proved to be the most simple and rapid procedure to remove traces of alpha-amylase from amyloglucosidase preparations. The apparent kinetic perameters of amyloglucosidase free of traces of alpha-amylase has been shown to be altered after inclusion of alpha-amylase. The increased apparent Km and V for the alpha-1,4-glucan/ amyloglucosidase/alpha-amylase system compared with those parameters for the system in the absence of alpha-amylase have been explained on the basis of the decrease in the size of the substrate molecule, which is caused by the action alpha-amylase (endo-attack pattern). The apparent kinetic perameters of amyloglucosidase oxidized traces of alpha-amylase has also substrates., Amyloglucosidase action has been established to be unable of by passing oxidation points introduced in the alpha-1,4-glucan by periodate oxidation. A theory has been developed to describe the action of amyloglucosidase on partially oxidized amylases, which predicts the decrease in the apparent Km and V with the increase in the degree of oxidation of the amylase, as it has been demonstrated experimentally. A direct recording method of assaying amyloglucosidase has been developed involving ascorbic acid as the oxygen acceptor in a glucose oxiddase/peroxidase assay system for glucose. This method permits amyloglucosidase activity to be followed by ultraviolet spectrophotometry. The merits and limitations of this procedure have been discussed. An immobilized cellulose derivative of amyloglucosidase in which the prosthetic group is involved in the covalent linkage between the enzyme end the support has been investigated and compared with the soluble enzyme. The kinetics, pH profile and the thermal stability of this immobilized enzyme and their comparison with these characteristics for the free enzyme have been investigated.

This thesis has attempted to describe some of the distribution patterns of submerged aquatic macrophytes in Scottish lochs. Effort has been directed towards prescribing a precise lochs. Effort has been directed towards prescribing a precise meaning to productivity with respect to these plants to its measurement, and to investigating presible influencing factors. Using aqualung diving techniques, biomass estimates have been made in several lochs. These results have been viewed in two ways, (a) qualitatively and (b) quantitatively. Qualitative It has been that, in any one loch, there is a zonation of species with depth of water. Generally, Littorella uniflora/Lobelia dortmanna communities were dominant in the shallower water (up to one metre), while otamogeton species occupied the deeper areas (up to seven metres). Of the substrate variables investigated, no parameters have been shown to be causally correlated with the distribution of such factors was complicated by a high degree of variance in the biomass estimates of vegetation on fairly uniform substrates. Distribution patterns of species between lochs have also been noted. The members of the Characeas were only found in the limestone lochs of high pH and alkalinity, while Lobelia dortmanna and Isoetes lacustris were confined to the more base-poor waters. Litorella uniflora was found in all the Iochs studied. Only two species of broad-leaved, sub-merged pondwecds were found in the limestone lochs but, while these were not restricted to such habitats, other species of the genus Potamogeton were. No one factor has been shown to underlie this distribution pattern though, in the case of the Characeae, it would appear that the high alkalinity of the water is related to the predominance of some members of this family in the limestone lochs, where they can produce their calcium carbonate exoskeletons. It is also possible that the low concentration of phosphorus in the limestone waters, shown by others to be a maximum factor in the growth of the Characase, is also important, while the general low nutrient concentrations may exclude other species from these areas.

It has become clear that the closed-field regions of the solar atmosphere are not static (as was once thought) but that many types of steady and unsteady flows and other dynamical, processes such as flares are continually occurring, in them. This thesis investigates some theoretical aspects of these dynamical phenomena. Steady, one-dimensional flow along a coronal loop is investigated first of all. Such a flow may be driven by a pressure difference between the foot points, and a wide range of shocked and unshocked flows are found. The presence of steady flows removes the symmetry present in most static loop models, and these models are shown to form only one class of a much wider range of dynamic solutions to the equations of motion. Thermal non-equilibrium in hot coronal loops occurs if the pressure in a loop becomes too big. The non-linear evolution of this non-equilibrium state is followed, and the loop is found to cool from of order 10[super]6 K to below 10[super]5 K in a few hours. An upflow is driven, and non-equilibrium is suggested as a means of formation of either cool loop cores or prominences. Thermal non-equilibrium is also discussed as a possible mechanism for the simple-loop flare. It is suggested that a cool equilibrium at a temperature of a few times 10[super]4 K can flare to over. 10[super]7 K if the mechanical heating in the cool loop becomes too large. The evolution is followed and the loop is found to flare to over 10[super]7 K in approximately 5 minutes. Magnetohydrodynamic shock waves have long been regarded as a potentially efficient heating mechanism. Their behaviour is re-examined here, and it is found that certain types of shock can release very large amounts of energy. These results are then applied to the heating of "post"-flare loops, for which temperatures of 10[super]7 K at the loop summit may be obtained. Finally, some solutions of the magnetostatic equation are discussed, and it is pointed out that if the gas pressure is too big then magnetostatic equilibrium will break down. It is suggested that the subsequent evolution may give rise to a surge or other mass ejection.

The field of the Chemistry of Starch is so wide and the complexities involved are so great that any attempt to solve the problems of the constitution of starch cannot be spread over the whole front, but must necessarily be confined to a few chosen points of attack. The following introduction, therefore, is not presented as a complete survey of literature of the subject but merely as a resumé of those parts bearing immediately on the topics studies, with special reference to the work of Dr. J. K. Rutherford, inasmuch as the present thesis is a continuation and amplification of her work.