The general subject of this thesis is quantum groups. The major original results are obtained in the particular areas of twisting constructions and noncommutative differential geometry. Chapters 1 and 2 are intended to explain to the reader what are quantum groups. They are written in the form of a series of linked results and definitions. Chapter 1 reviews the theory of Lie algebras and Lie groups, focusing attention in particular on the classical Lie algebras and groups. Though none of the quoted results are due to the author, such a review, aimed specifically at setting up the paradigm which provides essential guidance in the theory of quantum groups, does not seem to have appeared already. In Chapter 2 the elements of the quantum group theory are recalled. Once again, almost none of the results are due to the author, though in Section 2.10, some results concerning the nonstandard Jordanian group are presented, by way of a worked example, which have not been published. Chapter 3 concerns twisting constructions. We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner. In Chapter 4 we consider the differential calculus on Hopf algebras as introduced by Woronowicz. We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GL[sub]h,[sub]g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SL[sub]h(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensional bicovariant first order calculi on GL[sub]h,[sub]g(2) and that there is a single, unique, 3-dimensional bicovariant calculus on SL[sub]h(2). This 3-dimensional calculus may be obtained through a classical-like reduction from any one of the three families of 4-dimensional calculi on GL[sub]h,[sub]g(2). Details of the higher order calculi and also the quantum Lie algebras are presented for all calculi. The quantum Lie algebra obtained from the bicovariant calculus on SL[sub]h(2) is shown to be isomorphic to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian universal enveloping algebra U[sub]h(sl[sub]2(C)) and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module. We also obtain the quantum Killing form for this quantum Lie algebra.

Magnetic reconnection is a fundamental physical process by which stored magnetic energy may be released. It is already known that different reconnection regimes result from changes in the nature of the plasma inflow towards the reconnection site. In this thesis, we examine both how the outflow region responds to changes both in the inflow and outflow boundary conditions and also how introducing compressibility affects the results. We find that if the inflow is converging, the outflow velocity is least, the width of the outflow region is greatest and the ratio of outflowing thermal to kinetic energy is greatest. Also, there is one free outflow parameter which would naturally be specified by the velocity of plasma leaving the reconnection site. We suggest that reverse currents seen in numerical simulations may result from the specification of an extra boundary condition. In addition, we find that the main effects of including compressibility are: to enhance convergence or divergence of the inflow; to increase the maximum reconnection rate where the inflow is converging; to increase the flow speed near the reconnection site where the inflow is diverging; to give faster, narrower outflow jets; to increase variations between regimes in the energy conversion and to increase the ratio of thermal to kinetic energy in the outflow jet.

For the non-abelian simple groups G of order up to 106 , excluding the groups PSL(2,q), q > 9, the presentations in terms of an involution a and an element b of minimal order (with respect to a) such that G= < a,b > are well known. The presentations are complete in the sense that any pair (x,y) of generators of G satisfying x2=ym=1, with m minimal, will satisfy the defining relations of just one presentation in the list. There are 106 such presentations. Using a computer, we give generators for each maximal subgroup of the groups G. For each presentation of G, the generators of maximal subgroups are given as words in the group generators. Similarly generators for a Sylow p-subgroup of G, for each p, are given. For each group G, we give a representative for each conjugacy class of the group as a word in the group generators. Minimal presentations for each Sylow p-subgroup of the groups G, and for most of the maximal subgroups of G are constructed. To obtain such presentations, the Schur multipliers of the underlying groups are calculated. The same tasks are carried out for those groups PSL(2,q) of order less than 106 which are included in the "ATLAS of finite groups". For these groups we consider a presentation on two generators x, y with x2=y3=1. A finite group G is said to be efficient if it has a presentation on d generators and d+rank(M(G)) relations (for some d) where M(G) is the Schur multiplier of G. We show that the simple groups J1, PSU(3,5) and M22 are efficient. We also give efficient presentations for the direct products A5xA6, A5xA6,A6xA7 where Ĥ denotes the covering group of H.

Spectroscopic observations of 18 of the brighter Be and 0e stars in the Northern Hemisphere have been presented in this project. About 900 spectrograms were secured and measured using the more objective numerical technique (REDUCE and VCROSS) to obtain as many accurate radial velocities as possible for these stars. The analysis of these measurements has demonstrated clearly, that most of these early-type stars are indeed variable in radial velocity, while a real periodicity in the radial velocities of some of the programme stars is found. The long-term periodicities were attributed to the binary nature, while the short ones could be ascribed to the pulsation phenomenon. Orbital elements are determined for four newly discovered binary systems, and improved orbits are determined for four known binaries. Five other stars display short time-scale periodicity (less than 1.5 days) attributable to radial or non-radial pulsation, whilst three variables show little evidence for periodicity. Only two stars are found to have constant radial velocities. A brief summary of the properties of Be stars and all the available models to explain the Be phenomenon is presented in chapter one. Chapter two contains a brief description of the observing equipment and the techniques used. The reasons for selecting the programme stars are given in the same chapter. A complete explanation of the measuring technique used in this investigation is given in chapter three. In chapter four, all the analyses and the results for each star are given individually, while a discussion of previous work on these stars appears in the relevant sections. The final chapter contains a discussion of the results from this study together with an analysis of the energy distributions of the programme stars, compiled by the author from published fluxes and photometry from the ultraviolet to the infra-red parts of the electromagnetic spectrum. Some consideration of future work to be done on these types of stars is also given.

Carbohydrate metabolism and heterotrophic carbon fixation have been studied in the intertidal macrophytic brown algae Pelvetia canalioulata and Fucus spiralis. In neither of these species can the heterotrophic metabolism of glucose support net growths. Photosynthetic rate, however, is enhanced by over 40% in Pelvetia in the presence of exogenous glucose. It is postulated that this glucose lowers the light requirement for photosynthesis rather than acting as a substrate for significant levels of heterotrophic carbon fixation.

This thesis is concerned with the effects of magnetic atmospheres on solar oscillations. The behaviour of magnetohydrodynamic surface waves propagating on a single magnetic interface is discussed ignoring the effects of gravity. The effects of non-parallel propagation (where the wave vector is at an angle to the magnetic field direction) are considered. The effects of chromospheric magnetic fields on solar p- and f-modes in a stratified atmosphere are examined for three different models. In the first of these models, the chromosphere is assumed to be isothermal and permeated by a uniform and horizontal magnetic field. A dispersion relation for the p-modes trapped below such an atmosphere is derived. Asymptotic and numerical solutions for the p-modes are discussed in detail. An increase in chromospheric magnetic field strength leads to an increase in the frequency of the p-modes, whereas an increase in the chromospheric temperature leads to a decrease in the frequencies of these modes. Comparison with observational data suggests that both these effects may indeed take place. The second model is set up for magnetic fields which decrease with height in such a way that the Alfven speed remains constant. In addition to magnetic effects, the effects of non-parallel propagation on and f-modes are considered in the presence of such a non-uniform magnetic field. After deriving a very general dispersion relation, various asymptotic and numerical solutions have been obtained and the possible effects of magnetic fields and non-parallel propagation on these modes are examined. The presence of a horizontal non-uniform chromospheric field produces changes in the frequencies of the p- and f-modes, reducing the frequencies of p-modes and increasing the frequency of the f-mode. Besides depending upon magnetic field strength, frequencies also depend on both the mode's order n and its degree l. The effects of non-parallel propagation are found to be most significant for the f-mode and the low order p-modes. The magnetic structure of the chromosphere has been further generalised by combining the two models described above. In this three layer model, a dispersion relation is derived in a general manner and discussed in detail for the p-modes. The role of magnetoacoustic cut-off frequency is studied. Again, the results are qualitatively similar to those found from observation.

The vapour pressures of some inorganic sulphates at high temperatures were determined by the combined use of the Knudsen effusion, transpiration, and matrix isolation methods. After a detailed comparison with the results of other investigators, it is concluded that the principal vapour species in the case of K2SO4, Rb2SO4, and Cs2SO4 are the undecomposed sulphate molecules themselves, and in the case of Li2SO4 the decomposition products, Li, SO2, and O2. The sodium salt also decomposes to some extent into Na, SO2, and O2, but it is deduced that the vapour concentration of the species Na2O4 is probably greater than was formerly supposed. The decomposition of alkaline earth sulphates is also discussed, especially in the light of the dependence of the Knudsen effusion results upon the size of the orifice used. On the basis of the vapour constitutions deduced, thermodynamic functions for the important species present are tabulated up to 1400 K or above. Reference is also made to the function of sodium sulphate in the glass-making industry and to the possible mechanism of its corrosive action on furnace walls.

Formation flying is a new satellite mission concept that is concerned with clusters of satellites in neighboring orbits cooperating to perform a specific task. The tasks may be Earth observation or space-based interferometry where a cluster of small satellites is able to fulfill the same requirements as that of a larger, monolithic satellite. There exist a variety of models for the study of relative motion between two satellites. These include models based upon differential orbital elements, and relative position and velocity coordinates. Extensive work has been done on such models, both in the absence and presence of the J2 perturbation arising from the aspherical nature of the Earth, which causes variations in the orbital elements that describe the orbit. The approximate relative motion can be obtained analytically by using mean elements. However, the true orbit can only be described by the instantaneous osculating elements. An analytical method to propagate the relative motion between two satellites in highly elliptic orbits is the main focus of this thesis. The method is kinematically exact and it maintains a high degree of accuracy even in the presence of J2 perturbations. Mean orbital elements are used for orbit propagation, and expansions involving the powers of eccentricity are not utilized. The true anomaly of the reference satellite is treated as the independent variable, instead of time. The relative orbit kinematics are obtained by using a projection onto a unit sphere. This procedure allows the relative position variables to be treated as angles depending on the orbital element differences. The effect of adding short-period corrections due to J2 to the mean elements is also studied. Finally, the problem of formation reconfiguration is studied. The reconfiguration of a formation may be achieved by using impulsive thrust (velocity increments) or continuous control. This thesis presents a method to obtain the optimal velocity increments through numerical optimization, utilizing the analytical technique developed for relative orbit propagation. A continuous control law is also developed using a candidate Lyapunov function, and the asymptotic stability of the closed-loop system is ascertained.

<p>Essay 1 (with Tanja Kirjavainen and Roope Uusitalo) analyzes the effects of changes in school spending on changes in student performance. We use a large sample of matriculation examination scores of Finnish senior secondary school students from the years 1990–1998. We estimate fixed-effect panel data models that use the dramatic changes in the school spending caused by the 1990s' recession as identifying variation. According to the results, changes in teaching expenditure did not have a significant effect on the test scores. The grade point average in comprehensive school and the parents’ education are the strongest explanatory variables for student achievement.</p><p>Essay 2 examines which factors predict academic performance at university and compares the predictive values of subject-related entrance exams and indicators of past school performance. The results show that a large fraction of students would be admitted whether the admission was based on entrance exams, past performance or a combination of these, which is the current system. In the fields of engineering, social sciences and sport sciences entrance exams predict both graduation and the number of study credits after four years better than past school performance. In education past school performance is a better predictor of graduation. Changing the admission rule to school grades would affect the average student performance negatively in engineering and social sciences but positively in education. Using only entrance exams would not signifi-cantly change the average student performance in any field.</p><p>Essay 3 (with Roope Uusitalo) evaluates the changes in the times-to-degree at the Finnish universities in the 1990s. In particular, the study evaluates the effect of the 1992 student aid reform that was intended to shorten the duration of university studies. We find that the student aid reform had only a modest effect, and that this effect was limited to the fields with long median durations. Most of the decline in the observed times-to-degree can be explained by an increase in the unemployment rate that reduced student employment opportunities.</p><p>Essay 4 examines how university students' employment decisions affect their labor market success after graduation. The study is based on individual level panel data of Finnish university students from the years 1987–1998. The OLS estimates show that in-school work experience is associated with higher earnings and employment after graduation. Local unemployment rate during enrollment is used as an instrument for endogenous work experience acquisition. Comparing graduates with equal times-to-degree, the IV estimates show that work experience increases earnings considerably one year after graduation. The effect is smaller and statistically insignificant in later years. Taking into account that working usually leads to longer times-to-degree, IV estimates show no significant returns to student employment. </p>

Essay 1 (with Tanja Kirjavainen and Roope Uusitalo) analyzes the effects of changes in school spending on changes in student performance. We use a large sample of matriculation examination scores of Finnish senior secondary school students from the years 1990–1998. We estimate fixed-effect panel data models that use the dramatic changes in the school spending caused by the 1990s' recession as identifying variation. According to the results, changes in teaching expenditure did not have a significant effect on the test scores. The grade point average in comprehensive school and the parents’ education are the strongest explanatory variables for student achievement. Essay 2 examines which factors predict academic performance at university and compares the predictive values of subject-related entrance exams and indicators of past school performance. The results show that a large fraction of students would be admitted whether the admission was based on entrance exams, past performance or a combination of these, which is the current system. In the fields of engineering, social sciences and sport sciences entrance exams predict both graduation and the number of study credits after four years better than past school performance. In education past school performance is a better predictor of graduation. Changing the admission rule to school grades would affect the average student performance negatively in engineering and social sciences but positively in education. Using only entrance exams would not signifi-cantly change the average student performance in any field. Essay 3 (with Roope Uusitalo) evaluates the changes in the times-to-degree at the Finnish universities in the 1990s. In particular, the study evaluates the effect of the 1992 student aid reform that was intended to shorten the duration of university studies. We find that the student aid reform had only a modest effect, and that this effect was limited to the fields with long median durations. Most of the decline in the observed times-to-degree can be explained by an increase in the unemployment rate that reduced student employment opportunities. Essay 4 examines how university students' employment decisions affect their labor market success after graduation. The study is based on individual level panel data of Finnish university students from the years 1987–1998. The OLS estimates show that in-school work experience is associated with higher earnings and employment after graduation. Local unemployment rate during enrollment is used as an instrument for endogenous work experience acquisition. Comparing graduates with equal times-to-degree, the IV estimates show that work experience increases earnings considerably one year after graduation. The effect is smaller and statistically insignificant in later years. Taking into account that working usually leads to longer times-to-degree, IV estimates show no significant returns to student employment.