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Dissertations / Theses on the topic 'Topological vector spaces'
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1
Nielsen, Mark J. "Tilings of topological vector spaces /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5763.
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Vera, Mendoza Rigoberto. "Linear operations on locally convex topological vector spaces." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186699.
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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.
3
Pinchuck, Andrew. "Extension theorems on L-topological spaces and L-fuzzy vector spaces." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005219.
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A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.
4
Lear, Jeffrey Charles. "Barrelled spaces." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1993. http://www.kutztown.edu/library/services/remote_access.asp.
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Thesis (M.A.)--Kutztown University of Pennsylvania, 1993.Source: Masters Abstracts International, Volume: 45-06, page: 3171. Abstract precedes thesis title page as [2] preliminary leaves. Typescript. Includes bibliographical references (leaf 39).
5
Griesan, Raymond William. "Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184510.
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Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.
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Albuquerque, Nacib André Gurgel e. "Hardy-Littlewood/Bohnenblust-Hille multilinear inequalities and Peano curves on topological vector spaces." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7448.
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This work is divided in two subjects. The first concerns about the Bohnenblust-Hille and Hardy- Littlewood multilinear inequalities. We obtain optimal and definitive generalizations for both inequalities. Moreover, the approach presented provides much simpler and straightforward proofs than the previous one known, and we are able to show that in most cases the exponents involved are optimal. The technique used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this thesis to improve the constants for vector-valued Bohnenblust-Hille type inequalities. The second subject has as starting point the existence of Peano spaces, that is, Haurdor spaces that are continuous image of the unit interval. From the point of view of lineability we analyze the set of continuous surjections from an arbitrary euclidean spaces on topological spaces that are, in some natural sense, covered by Peano spaces, and we conclude that large algebras are found within the families studied. We provide several optimal and definitive result on euclidean spaces, and, moreover, an optimal lineability result on those special topological vector spaces.
Este trabalho édividido em dois temas. O primeiro diz respeito às desigualdades multilineares de Bohnenblust-Hille e Hardy-Littlewood. Obtemos generalizações ótimas e definitivas para ambas desigualdades. Mais ainda, a abordagem apresentada fornece demonstrações mais simples e diretas do que as conhecidas anteriormente, além de sermos capazes de mostrar que os expoentes envolvidos são ótimos em varias situações. A técnica utilizada combina ferramentas probabilísticas e interpolativas; esta ultima e ainda usada para melhorar as estimativas das versões vetoriais da desigualdade de Bohnenblust-Hille. O segundo tema possui como ponto de partida a existência de espaços de Peano, ou seja, os espaços de Hausdor que são imagem contínua do intervalo unitário. Sob o ponto de vista da lineabilidade, analisamos o conjunto das sobrejecoes contínuas de um espaço euclidiano arbitrário em um espaço topológico que, de certa forma, e coberto por espaços de Peano, e concluímos que grandes álgebras são encontradas nas famílias estudadas. Fornecemos vários resultados ótimos e definitivos em espaços euclidianos, e, mais ainda, um resultado de lineabilidade ótimo naqueles espaços vetoriais topológicos especiais.
7
Toolan, Timothy M. "Advances in sliding window subspace tracking /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3206257.
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Costa, Debora Cristina Brandt. "Operadores hipercíclicos em espaços vetoriais topológicos." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-01082007-115014/.
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Dado E um espaço vetorial topológico e T um operador linear contínuo em E, diremos que T é hipercíclico se, para algum elemento x pertencente a E, a órbita de x sob T, Orb(x,T)={x, Tx, T^2 x,...}, for densa em E. Nosso objetivo será apresentar alguns resultados sobre hiperciclicidade e observar como alguns espaços comportam-se diante dessa classe de operadores. \\\\Let E be a topological vector space and T a continuous linear operator on E. We say that T is hypercyclic if, for some x in E, the orbit of x on T, Orb(x,T)={x, Tx, T^2 x,...}, is dense in E. Our aim will be to study some results about hypercyclicity and to observe how some spaces behave regarding this class of operators.
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Cavalcante, Wasthenny Vasconcelos. "Espaços Vetoriais Topológicos." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9277.
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In this work we investigate the concept of topological vector spaces and their properties. In the rst chapter we present two sections of basic results and in the other sections we present a more general study of such spaces. In the second chapter we restrict ourselves to the real scalar eld and we study, in the context of locally convex spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak, weak-star, of bounded convergence and of pointwise convergence topologies. Finally we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and the Closed Graph Theorem.
Neste trabalho, estudamos o conceito de espa cos vetoriais topol ogicos e suas propriedades. No primeiro cap tulo, apresentamos duas se c~oes de resultados b asicos e, nas demais se c~oes, apresentamos um estudo sobre tais espa cos de forma mais ampla. No segundo cap tulo, restringimo-nos ao corpo dos reais e fazemos um estudo sobre os espa cos localmente convexos, o Teorema de Hahn-Banach, o Teorema de Banach- Alaoglu, constru mos as topologias fraca, fraca-estrela, da converg^encia limitada e da converg^encia pontual. Por ultimo, estudamos o Teorema da Limita c~ao Uniforme, o Teorema do Gr a co Fechado e o da Aplica c~ao Aberta no contexto mais geral dos espa cos de Fr echet.
10
Karliczek, Martin. "Elements of conditional optimization and their applications to order theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/17085.
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In dieser Arbeit beweisen wir für Optimierungsprobleme in L0-Moduln relevante Resultate und untersuchen Anwendungen für die Darstellung von Präferenzen. Im ersten Kapitel geht es um quasikonkave, monotone und lokale Funktionen von einem L0-Modul X nach L0, die wir robust darstellen. Im zweiten Kapitel entwickeln wir das Ekeland’sche Variationsprinzip für L0-Moduln, die eine L0-Metrik besitzen. Wir beweisen eine L0 -Variante einer Verallgemeinerung des Ekeland’schen Theorems. Der Beweis des Brouwerschen Fixpunktsatzes für Funktionen, die auf (L0)^d definiert sind, wird in Kapitel 3 behandelt. Wir definieren das Konzept des Simplexes in (L0)^d und beweisen, dass jede lokale, folgenstetige Funktion darauf einen Fixpunkt besitzt. Dies nutzen wir, um den Fixpunktsatz auch für Funktionen auf beliebigen abgeschlossenen, L0 -konvexen Mengen zu zeigen. Eine allgemeinere Struktur als L0 ist die bedingte Menge. Im vierten Kapitel behandeln wir bedingte topologische Vektorräume. Wir führen das Konzept der Dualität für bedingte Mengen ein und beweisen Theoreme der Funktionalanalysis darauf, unter anderem das Theorem von Banach-Alaoglu und Krein-Šmulian. Im fünften Kapitel widmen wir uns der Darstellung mit wandernden konvexen Mengen. Wir zeigen danach, wie die Transitivität für diese Darstellungsform beschrieben werden kann. Abschließend modellieren wir die Eigenschaft, dass die Transitivität einer Relation nur für ähnliche Elemente gesichert ist und diskutieren Arten der Darstellung solcher Relationen.In this thesis, we prove results relevant for optimization problems in L0-modules and study applications to order theory. The first part deals with the notion of an Assessment Index (AI). For an L0 -module X an AI is a quasiconcave, monotone and local function mapping to L0. We prove a robust representation of these AIs. In the second chapter of this thesis, we develop Ekeland’s variational principle for L0-modules allowing for an L0-metric. We prove an L0-Version of a generalization of Ekeland’s theorem. A further application of L0 -theory is examined in the third chapter of this thesis, namely an extension of the Brouwer fixed point theorem to functions on (L0)^d . We define a conditional simplex, which is a simplex with respect to L0 , and prove that every local, sequentially continuous function has a fixed point. We extend the fixed point theorem to arbitrary closed, L0-convex sets. A more general structure than L0 -modules is the concept of conditional sets. In the fourth chapter of the thesis, we study conditional topological vector spaces. We examine the concept of duality for conditional sets and prove results of functional analysis: among others, the Banach-Alaoglu and the Krein-Šmulian theorem. Any L0 -module being a conditional set allows to apply all results to L0 -theory. In the fifth chapter, we discuss the property of transitivity of relations and its connection to certain forms of representations. After a survey of common representations of preferences, we attend to relations induced by moving convex sets which are relations of the form that x is preferred to y if and only if x − y is in a convex set depending on y. We examine in which cases such a representation is transitive. Finally, we exhibit nontransitivity due to dissimilarity of the compared object and discuss representations for relations of that type.
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Fernandes, Vinicius de Souza. "O índice Maslov e suas aplicações em topologia simplética : a homologia de Floer e a conjectura de Arnold." reponame:Repositório Institucional da UFABC, 2018.
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12
"Some sort of barrelledness in topological vector spaces." Chinese University of Hong Kong, 1990. http://library.cuhk.edu.hk/record=b5886544.
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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
13
Helmstedt, Janet Margaret. "Closed graph theorems for locally convex topological vector spaces." Thesis, 2015. http://hdl.handle.net/10539/18010.
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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 ScienceLet 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
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Pinchuck, Andrew. "Extension theoroms on L-topological spaces and L-fuzzy vector spaces /." 2001. http://eprints.ru.ac.za/1301/.
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Sehgal, Kriti. "Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4913.
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Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand
the concept of holomorphicity of a complex-valued function. Suppose a function f defined
on O takes values in a locally convex topological vector space (the complex plane is one
particular example of a locally convex topological vector space). We want to study the notion
of holomorphicity for f in this general setting. In the paper “Sur certains espaces de fonctions
holomorphes I” [1], Alexandre Grothendieck deals with the concept of holomorphicity of
vector-valued functions and duality. We read, understand, reproduce and at times fill in
necessary details of the content of section 2 and a portion of section 4 of the paper.
We understand the extension of Lebesgue integral to vector-valued functions on a measure
space, named after I.M. Gelfand and B.J. Pettis as Gelfand-Pettis integral or Pettis integral
(page 77 in [2]). Using the definition of Pettis integral and some results from complex analysis
we introduce three notions of holomorphicity for the function f: holomorphicity of f on the
open set O, weak derivability of f at a point zo P O and strong differentiability of f at a
point zo P O.
In Chapter 2 (section 2 in [1]) of this thesis, we study the conditions under which the
first two notions of holomorphicity, i.e., f is holomorphic on the open set O and f is weakly
derivable at every point of O coincide. Further the same conditions will imply the strong
differentiability of f at each point of O. Also, we study Cauchy’s integral formula and
Taylor’s expansion for vector valued holomorphic functions in Chapter 2.
In section 4 of the paper “Sur certains espaces de fonctions holomorphes I” [1], for
a
subset of the Riemann sphere, Grothendieck introduces the space Pp
,Eq as the space of
all locally holomorphic functions on
vanishing at 8 if 8 P
. He further considers two
locally convex topological vector spaces E and F in separate duality and proves that the
spaces Pp
1,Eq and Pp
2, Fq, where
1 and
2 are complementary subsets of the Riemann
sphere, are in separate duality under some general conditions. In Chapter 3 of this thesis,
which constitute the main portion of the thesis, we study the space Pp
,Eq and further
present the argument of Grothendieck for separating duality with all details
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"Convex relations between topological vector spaces and adjoint convex processes." Chinese University of Hong Kong, 1989. http://library.cuhk.edu.hk/record=b5886159.
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"On generalizations of the Arrow-Barankin-Blackwell Theorem in vector optimization." 2000. http://library.cuhk.edu.hk/record=b5890336.
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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
18
Li, Ching-Yi, and 林靜宜. "Fixed Points of Multimaps On Admissible Almost Convex Sets In Topological Vector Spaces." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/88772115417887398913.
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碩士國立成功大學
數學系應用數學碩博士班
93
We use the concepts of generalized KKM mapping and the strict KKM property, which are recently introduced by J. C. Jeng, Y. Y. Huang and H. C. Hsu, to investigate the fixed point problem for T belong to SKKM(X,X) with X an admissible almost convex subset of a topological vector space E. We establish that if T belong to SKKM}(X,X) is compact and closed, then it has a fixed point. As applications of this new fixed point theorem, some results related to equilibrium problem in game theory are also deduced.
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"On density theorems, connectedness results and error bounds in vector optimization." 2001. http://library.cuhk.edu.hk/record=b5890681.
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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
20
Mandal, Samir Ch. "Dilation Theory of Contractions and Nevanlinna-Pick Interpolation Problem." Thesis, 2014. http://etd.iisc.ac.in/handle/2005/4110.
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In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's inequality'. Next we give a complete description of the dilation of a pure contraction. We also discuss Ando's proof of the existence of a unitary dilation of a pair of commuting contractions and give an example to show that this result does not hold, in general, for more than two commuting contractions. Then we describe and prove the `commutant lifting theorem' and lastly, we use this theorem to prove the operator valued `Nevanlinna-Pick interpolation problem'.
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Tshilombo, Mukinayi Hermenegilde. "Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces." Thesis, 2015. http://hdl.handle.net/10500/19942.
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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)
22
Černohorská, Eva. "Homotopické struktury v algebře, geometrii a matematické fyzice." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313715.
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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
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Кузнецова, Аліна Ігоревна. "Дослідження структури То-топологій малої ваги на скінченій множині." Магістерська робота, 2021. https://dspace.znu.edu.ua/jspui/handle/12345/6503.
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Кузнєцова А. І. Дослідження структури Т0-топологій малої ваги на скінченній множині : кваліфікаційна робота магістра спеціальності 111 "Математика" / наук. керівник П. Г. Стєганцева. Запоріжжя : ЗНУ, 2021. 42 с.UA : Кваліфікаційна робота магістра «Дослідження структури Т0-топологій малої ваги на скінченній множині»: 42 с., 3 рис., 20 джерел. Об’єкт дослідження – топології та їх структура. Мета роботи: узгодити термінологію і поняття з теми і упорядкувати систему означень, які найчастіше використовуватимемо у розділах, дослідити та описати властивості деяких видів скінченних топологічних просторів. Метод дослідження – аналітичний, порівняльний. Топологія займається вивченням властивостей геометричних об’єктів, які зберігаються при неперервних перетвореннях. У період з 1925-1975 рр. топологія була одним з основних предметів дослідження математиків з усього світу. Це пояснюється її великим значенням та можливістю досліджувати різні об’єкти без повного осягнення їх властивостей. У роботі розглянемо загальну топологію, а саме топологічні простори, які посідають важливе місце в сучасній математиці. Поняття топологічного простору можна сприймати як поняття геометричної фігури в широкому сенсі, в якому нам не важливі властивості типу розміру та точного положення фігури в просторі. Оскільки більшість типових прикладів топологічних просторів є просторами, які задовольняють аксіомі Т0, то тема дипломної роботи є актуальною.
EN : Master’s Qualification Thesis «Research of structure of Т0-topologies of small weight on a finite set»: 42 pages, 3 figures, 20 references. The object of the study is topologies and their structure. The aim of the study is to coordinate terminology and concept from a theme and put in order the system of determinations that mostly will use in divisions, prospect and describe properties of some types of eventual topological spaces The methods of research are analytical, comparative. A topology engages in the study of properties of geometrics, that is kept at continuous transformations. In a period from 1925-1975 a topology was one of the basic articles of research of mathematicians from the whole world. It is explained it by a large value and possibility to prospect different objects without the complete understanding of their properties. In-process will consider a general topology, namely topological spaces that occupy an important place in modern mathematics. The concept of topological space can be perceived as a concept of geometrical figure in wide sense in that not important properties us as a size and exact position of figure in space. As most typical examples of topological spaces are spaces that satisfy to the axiom of Т0, then a theme of diploma work is actual.
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Lopes, Pedro Manuel Antunes Faria. "Diagnóstico de Avarias e Tolerância a Falhas em Filtros Activos de Potência de 3 e 4 Fios, Baseados na Topologia Multinível NPC." Master's thesis, 2012. http://hdl.handle.net/10316/99531.
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Dissertação de Mestrado Integrado em Engenharia Electrotécnica e de Computadores apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra.Nos últimos anos, o mundo tem assistido a um grande desenvolvimento tecnológico marcado sobretudo pela proliferação de sistemas informáticos e de accionamentos eléctricos. No entanto, a utilização massiva deste tipo de cargas, ditas não-lineares, acarreta grandes problemas no que toca à qualidade da energia eléctrica, criando uma elevada poluição harmónica. Na tentativa de minimizar estes efeitos nocivos surgiram os filtros activos de potência, tradicionalmente compostos por um conversor de 2 níveis. Porém, devido aos recentes desenvolvimentos nas topologias multinível, estas começaram a integrar os sistemas de filtragem, conferindo-lhes um melhor desempenho. Contudo, uma vez que é usado um maior número de semicondutores, a probabilidade de ocorrência de uma falha de circuito aberto ou de curto-circuito num deles aumenta consideravelmente. Deste modo, surge a necessidade de desenvolver estratégias que permitam identificar estas avarias e actuar imediatamente de forma a que o sistema possa permanecer em funcionamento. No seguimento desta problemática, na presente dissertação irão ser propostos métodos de diagnóstico e de tolerância a falhas para filtros activos de potência paralelos de 3 e 4 fios, baseados num conversor NPC de 3 níveis. A validade das técnicas apresentadas irá ser comprovada através de simulações computacionais e de ensaios experimentais.
In the past few years, the world has witnessed a great technological development, where the computer systems and the electric drives play an important role. However, the massive widespread of this so called non-linear loads brings many problems regarding the electric power quality, creating a high harmonic pollution. In order to mitigate this harmful effect, the active power filters have appeared, traditionally composed by a 2 level converter. Nevertheless, due to recent development of multilevel topologies, they are becoming to integrate these filtering systems, improving their performance. However, since it is needed a greater number of switching devices, the probability of an open circuit or a short-circuit failure in one of them is significantly higher. Thus, it is important to develop strategies to identify these faults and act immediately in order to keep the system operational. Then, in this dissertation will be proposed fault diagnosis and fault tolerance methods for 3 and 4 wire shunt active power filters, based on a 3 level NPC converter. The effectiveness of these techniques will be demonstrated by simulation and experimental results.