Dissertations / Theses on the topic 'Linear topological vector space'

Our purpose is to extend, to the class of linear operators on a locally convex space, some of the results of spectral theory. In order to do this we had to introduce some topologies on the space of operators that are not locally convex. These topologies are of interest in their own right, and have proved useful in enabling us to attain our goal. There is an important class of topological vector spaces named ab-spaces (almost bornological spaces), but there are not too many facts about them. We briefly discuss some new results and give a characterization of those spaces in Chapter 3.

Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico
This research examined the teaching of concept of base of a vector space according to the premises mediated by Fedathi Sequence during the discipline âIntroduction to Algebraâ in the course of Engineering of Teleinformatic at Federal University of CearÃ. The objective was to determine whether the use of Fedathi Sequence specifically in classes about the concept of base provides resources capable of becoming Meta Lever, allowing students an education based on the reflection on the worked contents. In this sense, the investigation was conducted in the form of case study, having as subject the teacher of discipline, which allowed the observation during his classes and planning, as well as having granted an interview. The results indicated that the Fedathi Sequence favored the use of resources that could become Meta Lever for students, being decisive in mediating the teacher, once the teacher behavior to use it in the classroom motivates students to reflection. We consider theories ML and FS, in this research, are complementary, and therefore we indicate that the teacher know such tools and their potential for use in teaching of concept of base, awakening the teacher an awareness of the role of mediation suggested by Fedathi Sequence.
Esta pesquisa analisou o ensino da noÃÃo de base de um espaÃo vetorial mediado segundo os pressupostos da SequÃncia Fedathi durante a disciplina de IntroduÃÃo à Ãlgebra do curso de Engenharia de TeleinformÃtica da Universidade Federal do CearÃ. Objetivou-se verificar se o uso da SequÃncia Fedathi, especificamente, nas aulas sobre o conceito de base, proporciona recursos passÃveis de se tornarem Alavanca Meta, permitindo aos alunos um ensino baseado na reflexÃo sobre os conteÃdos trabalhados. Nesse sentido, a investigaÃÃo foi conduzida na forma de estudo de caso, tendo como sujeito o professor da disciplina, que permitiu a observaÃÃo durante suas aulas e planejamentos, alÃm de ter concedido uma entrevista. Os resultados encontrados apontaram que a SequÃncia Fedathi favoreceu o uso de recursos passÃveis de se tornarem Alavancas Meta para os alunos, sendo determinante na mediaÃÃo do professor, de modo que a postura docente ao utilizÃ-la em sala de aula motivava os alunos à reflexÃo. Consideramos que as teorias AM e SF, nessa pesquisa, se complementaram, e, portanto, indicamos que o professor conheÃa tais ferramentas e seu potencial de uso no ensino de base, despertando no professor uma consciÃncia do papel da mediaÃÃo preconizada pela SequÃncia Fedathi.

In this paper, we consider affine varieties in vector space to analyze and understand the geometric behavior of sets solutions of systems of linear equations, solutions of linear ordinary differential equations of second order resulting from mathematical modeling of systems, etc. We observed characteristics of affine varieties in vector spaces as a subspaces vector transferred to any vector belonging to affine variety and do a comparison of geometric representations of the solution sets of problem situations, cited above, with such features.
Neste trabalho, consideramos variedades afins no espaÃo vetorial para analisar e compreender o comportamento geomÃtrico de conjuntos soluÃÃes de sistemas de equaÃÃes lineares, de soluÃÃes de equaÃÃes diferenciais ordinÃrias lineares de segunda ordem resultantes de modelagens matemÃticas de sistemas, etc. Verificamos caracterÃsticas das variedades afins em espaÃos vetoriais como um subespaÃo vetorial transladado de qualquer vetor pertencente à variedade afim e fazemos uma comparaÃÃo das representaÃÃes geomÃtricas dos conjuntos soluÃÃes das situaÃÃes-problema, citados acima, com tais caracterÃsticas.

by Kin-Ming Liu.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1990.
Bibliography: leaves 66-67.
Chapter §0 --- Introduction
Chapter §1 --- Preliminaries and notations
Chapter §2 --- A summary on ultra-(DF)-spaces and order-ultra-（DF)-spaces
Chapter §3 --- " ""Dual"" properties between projective and inductive topologies in topological vector spaces"
Chapter §4 --- Application of barrelledness on continuity of bilinear mappings and projective tensor product
Chapter §5 --- Countably order-quasiultrabarrelled spaces

A Dissertation Submitted of the Faculty of Science, University of the Witwatersrand, Johannesburg in Partial Fulfilment of the Requirements for the Degree of Master of Science
Let 4 be the class of pairs of loc ..My onvex spaces (X,V) “h ‘ch are such that every closed graph linear ,pp, 1 from X into V is continuous. It B is any class of locally . ivex l.ausdortf spaces. let & w . (X . (X.Y) e 4 for ,11 Y E B). " ‘his expository dissertation, * (B) is investigated, firstly i r arbitrary B . secondly when B is the class of C,-complete paces and thirdly whon B is a class of locally convex webbed s- .ces

Chan Ka Wo.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (leaves 114-118).
Abstracts in English and Chinese.
Introduction --- p.iii
Conventions of This Thesis --- p.vi
Prerequisites --- p.xiii
Chapter 1 --- Cones in Real Vector Spaces --- p.1
Chapter 1.1 --- The Fundamentals of Cones --- p.2
Chapter 1.2 --- Enlargements of a Cone --- p.22
Chapter 1.3 --- Special Cones in Real Vector Spaces --- p.29
Chapter 1.3.1 --- Positive Cones --- p.29
Chapter 1.3.2 --- Bishop-Phelps Cones --- p.36
Chapter 1.3.3 --- Quasi-Bishop-Phelps Cones --- p.42
Chapter 1.3.4 --- Quasi*-Bishop-Phelps Cones --- p.45
Chapter 1.3.5 --- Gallagher-Saleh D-cones --- p.47
Chapter 2 --- Generalizations in Topological Vector Spaces --- p.52
Chapter 2.1 --- Efficiency and Positive Proper Efficiency --- p.54
Chapter 2.2 --- Type I Generalizations --- p.71
Chapter 2.3 --- Type II Generalizations --- p.82
Chapter 2.4 --- Type III Generalizations --- p.92
Chapter 3 --- Generalizations in Dual Spaces --- p.97
Chapter 3.1 --- Weak*-Support Points of a Set --- p.98
Chapter 3.2 --- Generalizations in the Dual Space of a General Normed Space --- p.100
Chapter 3.3 --- Generalizations in the Dual Space of a Banach Space --- p.104
Epilogue: Glimpses Beyond --- p.112
Bibliography --- p.114

Yung Hon-wai.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.
Includes bibliographical references (leaves 133-139).
Abstracts in English and Chinese.
Chapter 0 --- Introduction --- p.1
Chapter 1 --- Density Theorems in Vector Optimization --- p.7
Chapter 1.1 --- Preliminary --- p.7
Chapter 1.2 --- The Arrow-Barankin-Blackwell Theorem in Normed Spaces --- p.14
Chapter 1.3 --- The Arrow-Barankin-Blackwell Theorem in Topolog- ical Vector Spaces --- p.27
Chapter 1.4 --- Density Results in Dual Space Setting --- p.32
Chapter 2 --- Density Theorem for Super Efficiency --- p.45
Chapter 2.1 --- Definition and Criteria for Super Efficiency --- p.45
Chapter 2.2 --- Henig Proper Efficiency --- p.53
Chapter 2.3 --- Density Theorem for Super Efficiency --- p.58
Chapter 3 --- Connectedness Results in Vector Optimization --- p.63
Chapter 3.1 --- Set-valued Maps --- p.64
Chapter 3.2 --- The Contractibility of the Efficient Point Sets --- p.67
Chapter 3.3 --- Connectedness Results in Vector Optimization Prob- lems --- p.83
Chapter 4 --- Error Bounds In Normed Spaces --- p.90
Chapter 4.1 --- Error Bounds of Lower Semicontinuous Functionsin Normed Spaces --- p.91
Chapter 4.2 --- Error Bounds of Lower Semicontinuous Convex Func- tions in Reflexive Banach Spaces --- p.100
Chapter 4.3 --- Error Bounds with Fractional Exponents --- p.105
Chapter 4.4 --- An Application to Quadratic Functions --- p.114
Bibliography --- p.133

Title: Homotopic structures in algebra, geometry and mathematical physics Author: Eva Černohorská Department: Mathematical Institute of Charles University Supervisor: RNDr. Martin Markl, DrSc., Institute of Mathematics of the Academy of Sciences of the Czech Republic, Mathematical Institute of Charles University Abstract: The aim of this thesis was to generalize the result that associative algebras on finite dimensional vector spaces can be described using differentials on free algebras. This result is limited by the duality of vector spaces. If we assume that the underlying space has a linear topology, then we can use the duality between discrete and linearly compact (profinite) vector spaces. To generalize the notion of an algebra, we need to recall the completed tensor product on linear vector spaces. Since this topics does not seem to be sufficiently covered by the literature, this thesis could serve also as a comprehensive text on linear vector spaces and their completed tensor products. We prove that also A∞ structures on linearly compact vector spaces could be represented by differentials on a free algebra. Keywords: Strongly homotopy associative algebra, linear topological vector space, Pontryagin duality, completed tensor product, differential

Chee Shiu Chung = 阻尼振子的線空間結構與哈密頓理論 / 朱兆中.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 88).
Text in English; abstracts in English and Chinese.
Chee Shiu Chung = Zu ni zhen zi de xian kong jian jie gou yu ha mi dun li lun / Zhu Zhaozhong.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Conservative Systems --- p.4
Chapter 2.1 --- General Formalism --- p.4
Chapter 2.2 --- One Simple Harmonic Oscillator --- p.7
Chapter 2.3 --- Two Coupled Harmonic Oscillators --- p.9
Chapter 3 --- Dissipative Systems --- p.12
Chapter 3.1 --- Elimination of Bath --- p.12
Chapter 3.2 --- One Oscillator with Dissipation --- p.16
Chapter 3.3 --- Two Oscillators with Dissipation --- p.19
Chapter 4 --- Eigenvector Expansion and Bilinear Map --- p.21
Chapter 4.1 --- Formalism --- p.21
Chapter 4.2 --- Inner Product and Bilinear Map --- p.23
Chapter 4.3 --- Normalization and Phase --- p.25
Chapter 4.4 --- Matrix Representation --- p.25
Chapter 4.5 --- Duality --- p.28
Chapter 5 --- Applications and Examples of Eigenvector Expansion --- p.31
Chapter 5.1 --- Single Oscillator --- p.31
Chapter 5.2 --- Two Oscillators --- p.32
Chapter 5.3 --- Uneven Damping --- p.33
Chapter 6 --- Time Evolution --- p.36
Chapter 6.1 --- Initial-Value Problem --- p.36
Chapter 6.1.1 --- Green's Function --- p.37
Chapter 6.2 --- Sum Rules --- p.39
Chapter 7 --- Time-Independent Perturbation Theory --- p.41
Chapter 7.1 --- Non-degenerate Perturbation --- p.41
Chapter 7.2 --- Degenerate Perturbation Theory --- p.46
Chapter 8 --- Jordan Block --- p.48
Chapter 8.1 --- Jordan Normal Basis --- p.48
Chapter 8.1.1 --- Construction of Basis Vectors --- p.48
Chapter 8.1.2 --- Bilinear Map --- p.50
Chapter 8.1.3 --- Example of Jordan Normal Basis --- p.55
Chapter 8.2 --- Time Evolution --- p.56
Chapter 8.2.1 --- Time Dependence of Basis Vectors --- p.56
Chapter 8.2.2 --- Initial-Value Problem --- p.58
Chapter 8.2.3 --- Green's Function --- p.59
Chapter 8.2.4 --- Sum Rules --- p.60
Chapter 8.3 --- Jordan Block Perturbation Theory --- p.61
Chapter 8.3.1 --- Lowest Order Perturbation --- p.61
Chapter 8.3.2 --- Higher-Order Perturbation --- p.65
Chapter 8.3.3 --- Non-generic Perturbations --- p.66
Chapter 8.4 --- Examples of High-Order Criticality --- p.66
Chapter 8.4.1 --- Fourth-order JB --- p.67
Chapter 8.4.2 --- Third-order JB --- p.74
Chapter 8.4.3 --- Two Second-order JB --- p.79
Chapter 9 --- Conclusion --- p.81
Chapter A --- Appendix --- p.83
Chapter A.l --- Fourier Transform and Contour Integration --- p.83
Chapter B --- Degeneracy and Criticality --- p.86
Bibliography --- p.88

Multilevel inverters play a major role in the modern day medium and high power energy conversion processes. The classic two level voltage source inverter generates PWM pole voltage output having two levels with strong fundamental component and harmonics centered around the switching frequency and its multiples. With higher switching frequency, its components can be easily filtered and results in better Total harmonic distortion (THD) output voltage and current. But with higher switching frequency, switching loss of power devices increases and electromagnetic interferences also increases. Also in two level inverter, pole voltage switches between zero and DC bus volt-age Vdc. This switching results in high dv=dt and causes EMI and increased stress on the motor winding insulation. The attractive features of multilevel inverters compared to a two level inverter are reduced switching frequency, reduced switching loss, improved volt-age and current THD, reduced dv=dt, etc. Because of these reasons, multilevel invertersultilevelinvertersplayamajorroleinthemoderndaymediumandhighpower find application in electric motor drives, transmission and distribution of power, transportation, traction, distributed generation, renewable energy systems like photo voltaic, hydel power, energy management, power quality, electric vehicle applications, etc. AC motor driven applications are consuming the significant part of the generated electrical energy (more than 60%) around the world. The multilevel inverters are ideal for such applications, since the switching frequency of the devices can be kept low with lower out-put voltage dv=dt. Also by using multilevel inverters, the common mode voltage (CMV) switching can be made zero and associated motor bearing failure can be mitigated. For multilevel inverter topologies, as the number of level increases, the power circuit becomes more complex by the increase in the number of DC power supplies, capacitors, switching devices and associated control circuitry. The main focus of development in multilevel inverter for medium and high power applications is to obtain an optimized number of voltage levels with reduced number of switching devices, capacitors and DC power sources. In this thesis, a new hybrid seven level inverter topology with a single DC supply is proposed with reduced switch count. The inverter is realized by cascading two three level flying capacitor inverters with a half bridge module. Compared to the conventional seven level inverter topologies, the proposed inverter topology uses lesser number of semiconductor devices, capacitors and DC power supplies for its operation. For this topology, capacitor voltage balancing is possible for entire modulation range irrespective of the load power factor. Also capacitor voltage can be controlled over a switching cycle and this result in lowering the capacitor sizing for the proposed topology. A simple hysteresis band based capacitor voltage balancing scheme is implemented for the inverter topology. For a voltage source inverter fed induction motor drive system, the inverter pole voltage is the sum of motor phase voltage and common mode voltage. In induction motors, there exists a parasitic capacitance between stator winding and stator iron, and between stator winding and rotor iron. Common mode voltage with significant magnitude and high frequency switching causes leakage current through these parasitic capacitances and motor bearings. This leakage current can cause ash over of bearing lubricant and corrosion of ball bearings, resulting in an early mechanical failure of the drive system. In this thesis, analysis of extending the linear modulation range of a general n-level inverter by allowing reduced magnitude of common mode voltage (CMV) switching (only Vdc/18) is presented. A new hybrid seven level inverter topology, with a single DC supply and with reduced common mode voltage (CMV) switching is presented in this thesis for the first time. Inverter is operated with zero CMV for modulation index less than 86% and is operated with a CMV magnitude of Vdc/18 to extend the linear modulation range up to 96%. Experimental results are presented for zero CMV operation and for reduced common voltage operation to extend the linear modulation range. A capacitor voltage balancing algorithm is designed utilizing the pole voltage redundancies of the inverter, which works for every sampling instant to correct the capacitor voltage irrespective of load power factor and modulation index. The capacitor voltage balancing algorithm is tested for different modulation indices and for various transient conditions, to validate the proposed topology. In recent years, model predictive control (MPC) using the system model has proved to be a good choice for the control of power converter and motor drive applications. MPC predicts system behavior using a system model and current system state. For cascaded multilevel inverter topologies with a single DC supply, closed loop capacitor voltage control is necessary for proper operation. This thesis presents zero and reduced common mode voltage (CMV) operation of a hybrid cascaded multilevel inverter with predictive capacitor voltage control. For the presented inverter topology, there are redundant switching states for each inverter voltage levels. By using these switching state redundancies, for every sampling instant, a cost function is evaluated based on the predicted capacitor voltages for each phase. The switching state which minimizes cost function is treated as the best and is switched for that sampling instant. The inverter operates with zero CMV for a modulation index upto 86%. For modulation indices from 86% to 96% the inverter can operate with reduced CMV magnitude ( Vdc/18) and reduced CMV switching frequency using the new space-vector PWM (SVPWM) presented herein. As a result, the linear modulation range is increased to 96% as compared to 86% for zero CMV operation. Simulation and experimental results are presented for the inverter topology for various steady state and transient operating conditions by running an induction motor drive with open loop V/f control scheme. The operation of a two level inverter in the over-modulation region (maximum peak phase fundamental output of inverter is greater than 0:577Vdc) results in lower order harmonics in the inverter output voltage. This lower order harmonics (mainly 5th, 7th, 11th, and 13th) causes electromagnetic torque ripple in motor drive applications. Also these harmonics causes extra losses and adversely affects the efficiency of the drive system. Also inverter control becomes non linear and special control algorithms are required for inverter operation in the over modulation region. In conventional schemes, maximum fundamental output voltage possible is 0:637Vdc. In that case inverter is operated in a square wave mode, also called six-step mode. This operation results in high dv=dt for the inverter output voltage. With multilevel inverters also, the inverter operation with peak phase fundamental output voltage above 0:577Vdc results in lower order harmonics in the inverter output voltage and results in electromagnetic torque pulsation. In this thesis, a new space vector PWM (SVPWM) method to extend the linear modulation range of a cascaded five level inverter topology with a single DC supply is presented. Using this method, the inverter can be controlled linearly and the peak phase fundamental output voltage of the inverter can be increased from 0:577Vdc to 0:637Vdc without increasing the DC bus voltage and without exceeding the induction motor voltage rating. This new technique makes use of cascaded inverter pole voltage redundancy and property of the space vector structure for its operation. Using this, the induction motor drive can be operated till the full speed range (0 Hz to 50 Hz) with the elimination of lower order harmonics in the phase voltage and phase current. The ve level topology presented in this thesis is realized by cascading a two level inverter and two full bridge modules with floating capacitors. The inverter topology and its operation for extending the modulation range is analyzed extensively. Simulation and experimental results for both steady state and dynamic operating conditions are presented. Zero common mode voltage (CMV) operation of multilevel inverters results in reduced DC bus utilization and reduced linear modulation range. In this thesis two reduced CMV SVPWM schemes are presented to extend the linear modulation range by allowing reduced CMV switching. But using these SVPWM schemes the peak phase fundamental output voltage possible is only 0:55Vdc in the linear region. In this thesis, a method to extend the linear modulation range of a CMV eliminated hybrid cascaded multilevel inverter with a single DC supply is presented. Using this method peak fundamental voltage can be increased from 0 to 0:637Vdc with zero CMV switching inside the linear modulation range. Also inverter can be controlled linearly for the entire modulation range. Also, various PWM switching sequences are analyzed in this thesis and the PWM sequence which gives minimum current ripple is used for the zero CMV operation of the inverter. The inverter topology with single DC supply is realized by cascading a two level inverter with two floating capacitor fed full bridge modules. Simulation and experimental results for steady state and dynamic operating conditions are presented to validate the proposed method. A three phase, 400 V, 3.7 kW, 50 Hz, two-pole induction motor drive with the open-loop V/f control scheme is implemented in the hardware for testing proposed inverter topology and proposed SVPWM algorithms experimentally. The semiconductor switches that were used to realize the power circuit for the experiment were 75 A, 1200 V IGBT half-bridge modules (SKM-75GB-12T4). Optoisolated gate drivers with de-saturation protection (M57962L) were used to drive the IGBTs. For the speed control and PWM timing computation, TMS320F28335 DSP is used as the main controller and Xilinx SPARTAN-3 XC3S200 FPGA as the PWM signal generator with dead time of 2.5 s. Level shifted carrier-based PWM algorithm is implemented for the normal inverter operation and zero CMV operation. From the PWM algorithm, information about the pole voltage levels to be switched can be obtained for each phase. In the sampling period, for capacitor voltage balancing of each phase, the DSP selects a switching state using the capacitor voltage information, current direction and pole voltage data for each phase. This switching state information along with the PWM timing data is sent to an FPGA module. The FPGA module generates the gating signals with a dead time of 2.5 s for the gate driver module for all the three phases by processing the switching state information and PWM signals for the given sampling period. For fundamental frequencies above 10Hz, synchronous PWM technique was used for testing the inverter topology. For modulation frequencies 10Hz and below, a constant switching frequency of 900 Hz was used. Various steady state and transient operation results are provided to validate the proposed inverter topology and the zero and reduced CMV operation schemes and extending the linear modulation scheme presented in this thesis. With the advantages like reduced switch count, single DC supply requirement, zero and reduced CMV operation, extension of linear modulation range, linear control of induction motor over the entire modulation range with zero CMV, lesser dv=dt stresses on devices and motor phase windings, lower switching frequency, inherent capacitor balancing, the proposed inverter power circuit topologies, and the SVPWM methods can be considered as good choice for medium voltage, high power motor drive applications.

My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic polynomial of a matroid are encoded in the f-vector of the broken circuit complex of the matroid. Among main results of the thesis are characterizations of the complete intersection and Gorenstein properties of the broken circuit complex and the Orlik-Terao algebra. I also study the h-vector of the broken circuit complex of a series-parallel network and relate certain entries of that vector to ear decompositions of the network. An application of the Orlik-Terao algebra in studying the relation space of a hyperplane arrangement is also included in the thesis.

This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures.
Mathematical Sciences
D. Phil. (Mathematics)