The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this thesis, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the Cowen-Douglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the Cowen-Douglas class. Secondly, we obtain an explicit formula for the curvature of the jet bundle of the Hermitian holomorphic bundle E f on a planar domain Ω. Here Ef is assumed to be a pull-back of the tautological bundle on gr(n, H ) by a nondegenerate holomorphic map f :Ω →Gr (n, H ). Clearly, finding relationships amongs the complex geometric invariants inherent in the short exact sequence 0 → Jk(Ef ) → Jk+1(Ef ) →J k+1(Ef )/ Jk(Ef ) → 0 is an important problem, whereJk(Ef ) represents the k-th order jet bundle. It is known that the Chern classes of these bundles must satisfy c(Jk+1(Ef )) = c(Jk(Ef )) c(Jk+1(Ef )/ Jk(Ef )). We obtain a refinement of this formula: trace Idnxn ( KJk(Ef )) - trace Idnxn ( KJk-1(Ef ))= KJk(Ef )/ Jk-1(Ef )(z).

It has become increasingly clear that dealing with present day environmental crises requires a holistic view that takes into account the interactions of social and ecological factors across multiple spatial and temporal scales. An example of where this new paradigm is being operationalized is the study of social-ecological systems. A substantial aspect of this growing research area aims to contribute to a more comprehensive understanding of the links between social-ecological systems, the ecosystem services they generate, and human well-being. This thesis summarizes the first part of a PhD project with the overall objective of unravelling some of these linkages using a mapping approach in South Africa, a country with high levels of social and ecological diversity. In the first paper, I present an approach to mapping social-ecological systems based on different bundles of ecosystem services. Mapping social-ecological systems has so far mainly been achieved by the overlay of separate social and ecological data. Here, I identify characteristic bundles of ecosystem services and use these bundle types as a proxy for different social-ecological systems in South Africa. The emergent pattern shows three distinct and spatially coherent systems that represent an overall low, medium and high level of ecosystem service use amongst households, and differs markedly from maps based on the overlay of social and ecological datasets. This approach not only identifies areas within South Africa where people are especially vulnerable to environmental changes that negatively affect ecosystem services, but also highlights areas in which distinctly different system dynamics operate in close proximity. It is especially in those areas where systems characterized by high and low dependence on ecosystem services lie side by side that nuanced and differentiated decision-making is required to sustainably manage ecosystem services in support of human well-being across all sectors of society. In the second paper I expand on the approach pioneered in Paper I by mapping human well-being bundles in South Africa. Mapping human well-being as bundles allows us to interrogate the trade-offs between different constituents of well-being at the sub-national scale, something that is not possible when measuring human well-being based on indicators or indices that reduce well-being to a single number. This approach also enables us to perform a spatial comparison between the levels of ecosystem service use (identified in Paper I) and human well-being, which signifies an important step forward in the development of quantitative tools for the analysis of the relationship between ecosystem services and human well-being at scales between the local and the national. / Governance of ecosystem services under scenarios of change in southern and eastern Africa

This thesis describes the development of a Mach-Zehnder interferometric filter based planar Doppler velocimetry (MZI-PDV) flow measurement technique. The technique uses an entirely new optical system, an unbalanced MZI incorporating glass blocks for wavefront-matching, to replace the iodine cell currently used in conventional PDV. The free spectral range of the interferometric filter can be selected by adjusting the optical path difference of the MZI. This allows the velocity measurement range, sensitivity and resolution to be varied. This system offers no restricts to the choice of laser wavelength of operation which is not the case with most techniques. Two techniques to process the interference fringe images are presented. The first uses the shift of the fringe pattern to determine the Doppler frequency shift along profiles. The second provides a full-field measurement by normalising the received light intensity at each pixel in the image. With the single camera MZI-PDV scheme, exact alignment of the two output images on the active area of the camera is automatic. This eliminates the pixel-matching problem in conventional two camera PDV systems. The technique allows the measurement of up to three components of the flow velocity across a plane defined by a laser light sheet. The construction of a single velocity component MZI-PDV system that incorporates a phase-locking system designed to stabilise the filter is described. Measurements are made on the velocity field of a rotating disc with maximum velocities of ~±70ms-1 and an axis-symmetric air jet (with a nozzle diameter of 20mm) with an exit velocity of ~85ms-1. Standard deviations in the measured velocities were found to be about 2.9 and 2ms-1 for the two processing methods respectively. The system was then modified to make 3-component velocity measurements using imaging fibre bundles to port multiple views to a single detector head, and the standard deviation of the velocity error is around ±3ms-1 for a maximum velocity of ~±30ms-1 in the field of view. The factors that will affect the quality of the interference fringe image are investigated including polarisation sensitivity of the two beam splitters and flatness of the optical components. The inclination angle and the optical path deviation have little effect on the contrast of the interference fringes since collimated light beams, rather than divergent ones, are used in the interferometer.

This thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions is described and the relevant geometric machinery explained. The necessary Clifford algebra is established and applied to understand the relationship between the spinor bundles of the base, the fibres and the total space of a submersion. O'Neill-type formulae relating the covariant derivatives of spinor fields on the base and fibres to the corresponding spinor field on the total space are derived. From these, formulae for the Dirac operators are obtained and applied to prove results on Dirac morphisms in cases so far unpublished. The second part (comprising chapters 7-9) contains the basic theory and known classifications of G2-structures and Spin+ 7 -structures in seven and eight dimensions. Formulae relating the covariant derivatives of the canonical forms and spinor fields are derived in each case. These are used to confirm the expected result that the form and spinorial classifications coincide. The mean curvature vector of associative and Cayley submanifolds of these spaces is calculated in terms of naturally-occurring tensor fields given by the structures. The final part of the thesis (comprising chapter 10) is an attempt to unify the first two parts. A certain `7-complex' quotient is described, which is analogous to the well-known hyper-Kahler quotient construction. This leads to insight into other possible interesting quotients which are correspondingly analogous to quaternionic-Kahler quotients, and these are speculated upon with a view to further research.

The topic of this thesis is the moduli theory of (parabolic) sheaves on stable curves. Using geometric invariant theory (GIT), universal moduli spaces of semistable parabolic sheaves on stable marked curves are constructed: `universal' indicates that these are moduli spaces of pairs where the underlying marked curve may vary as well as the parabolic sheaf (as in the Pandharipande moduli space for pairs of stable curves and torsion-free sheaves without augmentations). As an intermediate step in this construction, we construct moduli spaces of semistable parabolic sheaves on flat families of arbitrary projective schemes (of any dimension or singularity type): this is the technical core of this thesis. These moduli spaces are projective, since they are constructed as GIT quotients of projective parameter spaces. The stability condition for parabolic sheaves depends on a choice of polarisation and is derived from the Hilbert-Mumford criterion. It is not quite the same as traditional stability with respect to parabolic Hilbert polynomials, but it is closely related to it, and the resulting moduli spaces are always compactifications of moduli of slope-stable parabolic sheaves. The construction works over algebraically closed fields of arbitrary characteristic.

In this thesis we study various ways in which every two general points on a variety can be connected by curves of a fixed genus, thus mimicking the notion of a rationally connected variety but for arbitrary genus. We assume the existence of a covering family of curves which dominates the product of a variety with itself either by allowing the curves in the family to vary in moduli, or by assuming the family is trivial for some fixed curve of genus g. A suitably free curve will be one with a large unobstructed deformation space, the images of whose deformations can join any number of points on a variety. We prove that, at least in characteristic zero, the existence of such a free curve of higher genus is equivalent to the variety being rationally connected. If one restricts to the case of genus one, similar results can be obtained even allowing the curves in the family to vary in moduli. In later chapters we study algebraic properties of such varieties and discuss attempts to prove the same rational connectedness result in positive characteristic.

Despite the significance of understanding the reasons under which talented individuals are more likely or less likely to quit, the nature of the relationship between Human Resource Management Practices (HRMPs) and turnover intentions has proven to be unclear. Prior studies suggest that talented employees’ turnover imposes significant negative impact on organisational performance, e.g. decrease in productivity, profitability, innovation, serviceability and morale of remaining employees. Likewise, a serious talented Frontline Managers (FLMs) turnover is observed in the private banks of Pakistan. The corresponding reason identified is their dissatisfaction with existing conventional HRMPs, which are typically bureaucratic in nature with no provision of training and development, and lack appreciation, seniority-based pay and promotions. Owing to these factors, FLMs are switching towards reputable government and multinational organisations. In fact, FLMs play an important role in the development and success of banks. To investigate this issue, the present study elaborates an examination of the use of synergistic HRMPs in an on-going effort to control the talented FLMs’ turnover intentions. Precisely, it examines the impact of two formative bundles, namely, skills-enhancing practices (SEPs, i.e. training and development) and motivation-enhancing practices (MEPs, i.e. pay, promotion, recognition and job security) on FLMs’ turnover intentions through organisational commitment. The research methodology employs a positivist philosophy, deductive approach and a quantitative method followed by a survey-based research design. A total of 500 questionnaires were distributed through random sampling technique; 344 questionnaires were finalised for analysis. PLS-SEM was used to test the research hypotheses. Contrary to conventional wisdom, the findings of this study indicate that both SEPs and MEPs demonstrate no significant direct impact on talented FLMs’ turnover intentions. However, organisational commitment (OC) has been found to fully mediate the relationships between both HRM bundles and FLMs’ turnover intentions. This research contributes to HRM literature particularly in the area of HRMPs—Turnover relationships. Furthermore, this study reveals that socio-economic relationships can be used to influence FLMs’ OC and turnover intentions. The findings further suggest that adoption of effective SEPs and MEPs in local banks enhance talented FLMs’ skills and motivation which eventually reduce their turnover intentions. Additionally, this study highlights the important and critical role of OC in HRMPs—turnover relationships, particularly in the Pakistani banking sector and further recommends management to review their HRMPs, which not only tend to reduce turnover but also lead to FLMs’ enhanced enthusiasm to serve.

A cultural tour package is essentially a travel package that bundles tourism products and services together with themes based on the destination's culture. Winnipeg's Cultural Tour Package Research project, proposed by Winnipeg Symphony Orchestra (WSO), is a project aiming to structure a tourism package centered at Winnipeg's performing arts and cultural attractions. Through the program, we identify customers' preference for the cultural items as well as the factors related to the preference. We also provide a marketing plan suggesting the direction of starting the program based on SWOT and marketing mix analyses. The research is contributable to both the marketing and the cultural tourism literatures. Also, in practical, the research stands at a macro level to demonstrate the benefits of integrating cultural items in Winnipeg and to suggest ways for WSO to cooperate with other cultural or supporting institutions to offer the program. / October 2015

Stocker de grandes quantités de données complexifie les interactions avec les systèmes de Business Intelligence (BI). Les systèmes de recommandation semblent un choix logique pour aider les utilisateurs dans leur analyse. Ils extraient des comportements de données historiques et suggèrent des actions personnalisées, potentiellement redondantes, via des scores de similarité. La diversité est essentielle pour améliorer la satisfaction des utilisateurs, d’où l’intérêt particulier accordé aux recommandations complémentaires. Nous avons étudié deux problèmes concrets d’exploration de données en BI et proposons de découvrir et exploiter les intentions utilisateur pour fournir deux recommandeurs de requête. Le premier, un recommandeur collaboratif réactif original basé sur l’intention, recommande des séquences de requêtes à l’utilisateur pour poursuivre son analyse. Le second propose proactivement un ensemble de requêtes pour compléter un rapport BI, en fonction di contexte utilisateur. / The storage of big amounts of data may lead to a series of long questions towards the expected solution which complicates user interactions with Business Intelligence (BI) systems. Recommender systems appear as a natural solution to help the users complete their analysis. They try to discover user behaviors from the past logs and to suggest personalized actions by predicting lists of likeness scores, which may lead to redundant recommendations. Nowadays, diversity is becoming essential to improve users’ satisfaction, thus, a special interest is dedicated to complementary recommendation. We studied two concrete data exploration problems in BI and we propose to discover and leverage the user intents to provide two query recommenders. The first, an original reactive collaborative Intent-based Recommender, recommends sequences of queries for the user to pursue her analysis. The second one proactively proposes a bundle of queries to complete user BI report, based on the user intents.

Bundles and morphisms between bundles are defined in the category of Fr¨olicher spaces (earlier known as the category of smooth spaces, see [2], [5], [9], [6] and [7]). We show that the sections of Fr¨olicher bundles are Fr¨olicher smooth maps and the fibers of Fr¨olicher bundles have a Fr¨olicher structure. We prove in detail that the tangent and cotangent bundles of a n-dimensional pseudomanifold are locally diffeomorphic to the even-dimensional Euclidian canonical F-space R2n. We define a bilinear form on a finite-dimensional pseudomanifold. We show that the symplectic structure on a cotangent bundle in the category of Fr¨olicher spaces exists and is (locally) obtained by the pullback of the canonical symplectic structure of R2n. We define the notion of symplectomorphism between two symplectic pseudomanifolds. We prove that two cotangent bundles of two diffeomorphic finite-dimensional pseudomanifolds are symplectomorphic in the category of Frölicher spaces.