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1
Wong, Chin Pin. "Kato's Perturbation Theorem and honesty theory". Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:c72c308b-d96d-4e31-a854-f2a10e99eeb6.
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We study an additive perturbation theorem for substochastic semigroups which is known as Kato's Theorem. There are two previously-known generalisations of Kato's Theorem, namely for abstract state spaces and for KB-spaces. We prove a version of Kato's Theorem for a class of spaces which encompasses both, namely ordered Banach spaces with generating cone and monotone norm. We also study a property of the perturbed semigroup in Kato's Theorem known as honesty of the semigroup. We add a few results to the fairly extensive existing theory of honesty for Kato's Theorem for abstract state spaces. In light of our new generalisation of Kato's Theorem to ordered Banach spaces with monotone norm, we investigate generalising the theory of honesty to these spaces as well. The results for the general case are less complete as many of the results for the case of abstract state spaces depend on the additive norm structure of the space. We also consider some new applications of honesty theory in abstract state spaces. We begin by applying honesty theory to the study of the heat equation on graphs. We prove that honesty of the heat semigroup coincides with a concept known as stochastic completeness of the graph which has been studied independently of honesty. We then look at the application of honesty theory to quantum dynamical semigroups. We show that honesty is the natural generalisation of the concept of conservativity of quantum dynamical semigroups. Conservative quantum dynamical semigroups are known to have certain "nice" properties. We show that similar properties hold for honest semigroups using honesty theory results. Finally, we consider a form of boundary perturbations in the context of transport semigroups. There exists an analogous theory of honesty for this set-up. We formulate a general result from which honesty results of both Kato's Theorem and transport semigroups can be derived.
2
Gomaa, Walid. "Model theory and complexity theory". College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7227.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Computer Science. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
3
Takeda, Yuichiro. "Localization theorem in equivariant algebraic K-theory". 京都大学 (Kyoto University), 1997. http://hdl.handle.net/2433/202419.
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Adams, Damien. "Galois theory and the Hilbert Irreducibility Theorem". Thesis, San Jose State University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=1541481.
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We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theory and Hilbert's Irreducibility Theorem: given any irreducible polynomial f(t1, t 2, …, tn, x) over the rational numbers, there are an infinite number of rational n-tuples (a 1, a2, …, an) such that f(a1, a2, …, an, x) is irreducible over the rational numbers.
We take a preliminary look at linear algebra, symmetric groups, extension fields, splitting fields, and the Chinese Remainder Theorem. We follow this by studying normal extension fields and Galois theory, proving the fundamental theorem and some immediate consequences. We expand on Galois theory by exploring subnormal series of subgroups and define solvability with group property P, ultimately proving Galois' Theorem. Beyond this, we study symmetric functions and large extension fields with Galois group Sn.
We detour into complex analysis, proving a few of Cauchy's theorems, the identity theorem, which is a key to proving Hilbert's Irreducibility Theorem, and meromorphic functions. We study affine plane curves, regular values, and the Density Lemma—which bounds the rational outputs a non-rational meromorphic function has for rational inputs. Ultimately, we prove the Hilbert Irreducibility Theorem and apply it to symmetric functions to construct fields whose Galois group is Sn.
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Mellquist, Ebba. "Galois Theory and the Artin-Schreier Theorem". Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414097.
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Smith, Stephen D. "Theory against itself : literary theory and the limits of theory". Thesis, University of Nottingham, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334294.
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Ali, T. "String theory and conformal field theory". Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595446.
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In this thesis we consider some aspects of two dimensional Conformal Field Theory and their connection to String Theory. We have also studied some aspects of supersymmetry of M-Theory on Ricci-flat seven manifolds with 4-form fluxes. We concentrate mainly on certain supersymmetric extensions of the coset models due to Goddard, Kent and Olive (GKO). These models are known as the Kazama-Suzuki (KS) models and they are characterized by their N = 2 superconformal symmetry. Two series of the KS models enjoy a duality called level-rank duality which can be described roughly as duality between the dimension of the target space and the level of coset. We believe that the path-integral approach is the closest in spirit to string theory. Therefore, we formulate the level-rank duality of KS models in the path-integral approach by using the realization of GKO cosets as gauged Wess-Zumino-Novikov-Witten (gauged-WZNW) models. We derive, for a class of KS models, an expression for the partition function which is symmetric in the parameters of the level-rank duality. We compute the central charge of the models from this expression which matches that of Kazama and Suzuki in the operator approach. We then work out the target space metric and the dilation of the gauged-WZNW model based on the GKO coset SU(3)/(SU(2) x U(1)). It turns out to be quite a complicated metric with a non-trivial dilation. We verify, as a consistency check, that they satisfy the appropriate string theory effective equations of motion. We then argue that this background can arise naturally in type II string theory compactified down to AdS3 space. We then turn to Eleven Dimensional Supergravity which is the low energy limit of M-theory. We adopt a metric ansatz which is a warped product of four dimensional Minkowski space and a (non-compact) seven manifold with 4-form fluxes turned on it. We derive the condition for unbroken supersymmetry with fluxes and non-trivial warp-factor. We show that the same condition implies that the seven manifold is conformal to a Ricci-flat manifold. We also point out the limitation of some naive ansatze about the structure of the Killing spinor. At this stage we are unable to give an explicit solution to the supersymmetry condition.
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Levikov, Filipp. "L-theory, K-theory and involutions". Thesis, University of Aberdeen, 2013. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=201918.
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In Part 1, we consider two descriptions of L-homology of a (polyhedron of a) simplicial complex X. The classical approach of Ranicki via (Z,X)-modules (cf. [Ran92]) iswell established and is used in Ranicki’s definition of the total surgery obstruction and his formulation of the algebraic surgery exact sequence (cf. [Ran79], [Ran92],[KMM]). This connection between algebraic surgery and geometric surgery has numerous applications in the theory of (highdimensional) manifolds. The approach described in [RW10] uses a category of homotopy complexes of cosheaves to construct for a manifold M a (rational) orientation class [M]L• in symmetric L-homology which is topologically invariant per construction. This is used to reprove the topological invariance of rational Pontryagin classes. The L-theory of the category of homotopy complexes of sheaves over an ENR X can be naturally identified with L-homology of X. If X is a simplicial complex, both definitions give L-homology, there is no direct comparison however. We close this gap by constructing a functor from the category of (Z,X)-modules to the category of homotopy cosheaves of chain complexes of Ranicki-Weiss inducing an equivalence on L-theory. The work undertaken in Part 1 may be considered as an addendum to [RW10] and suggests some translation of ideas of [Ran92] into the language of [RW10]. Without significant alterations, this work may be generalised to the case of X being a △-set. The L-theory of △-sets is considered in [RW12]. Let A be a unital ring and I a category with objects given by natural numbers and two kinds of morphisms mn → n satisfying certain relations (see Ch.3.4). There is an I-diagram, given by n 7→ ˜K (A[x]/xn) where the tilde indicates the homotopy fiber of the projection induced map on algebraic K-theory (of free modules) K(A[x]/xn) → K(A). In Part 2 we consider the following result by Betley and Schlichtkrull [BS05]. After completion there is an equivalence of spectra TC(A)∧ ≃ holim I ˜K(A[x]/xn)∧ where TC(A) is the topological cyclic homology of A. This is a very important invariant of K-theory (cf. [BHM93], [DGM12]) and comes with the cyclotomic trace map tr : K(A) → TC(A). In [BS05], the authors prove that under the above identification the trace map corresponds to a “multiplication” with an element u∞ ∈ holim I ˜K (Z[x]/xn). In this work we are interested in a generalisation of this result. We construct an element u∞ ∈ holim I ˜K(Cn). where Cn can be viewed as the category of freemodules over the nilpotent extension S[x]/xn of the sphere spectrum S. Let G be a discrete group and S[G] its spherical group ring. Using our lift of u∞ we construct a map trBS : K(S[G]) → holim I ˜K (CG n ) where CG n should be interpreted as the category of free modules over the extension S[G][x]/xn. After linearisation this map coincides with the trace map constructed by Betley and Schlichtkrull. We conjecture but do not prove, that after completion the domain coincides with the topological cyclic homology of S[G]. Some indication is given at the end of the final chapter. To construct the element u∞ we rely on a generalisation of a result of Grayson on the K-theory of endomorphisms (cf. [Gra77]). Denote by EndC the category of endomorphisms of finite CW-spectra and by RC the Waldhausen category of free CW-spectra with an action of N, which are finite in the equivariant sense. Cofibrations are given by cellular inclusions and weak equivalences are given bymaps inducing an equivalence of (reduced) cellular chain complexes of Z[x]-modules, after inverting the set {1 + xZ[x]}. In Chapter 5 we prove (5.8) that there is a homotopy equivalence of spectra ˜K (EndC) ≃ ˜K (RC). where tildes indicate that homotopy fibres of the respective projections are considered. Furthermore, we pursue the goal of constructing an involutive tracemap for themodel of [BS05]. We employ the framework ofWaldhausen categories with duality (cf. [WW98]) to introduce for any G involutions on holim I ˜K (CG n ). We give enough indication for our trace map being involutive, in particular in the last three sections of Chapter 5, we sketch how the generalisation of the theoremof Grayson (5.8) can be improved to an involutive version. In the final chapter, we develop this further. Assuming that the element u∞ ∈ holim I ˜K (Cn) is a homotopy fixed point of the introduced involution, we construct a map from quadratic L-theory of S[G] to the Tate homology spectrum of Z/2 acting on the fibre of trBS (see 6.9) : L•(S[G]) → (hofib(trBS))thZ/2 and discuss the connection of this to a conjecture of Rognes andWeiss. The two parts of the thesis are preluded with their own introduction andmay be read independently. The fewcross references are completely neglectible.
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Palmer, Sam. "Higher gauge theory and M-theory". Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/3054.
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In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loops on spacetime. This construction maps solutions of the Basu-Harvey equation, the BPS equation arising in the description of multiple M2-branes, to solutions of a selfdual string equation on loop space. Furthermore, all ingredients of the construction reduce to those of the ordinary Nahm construction when compactified on a circle with all loops restricted to those wrapping the circle. The rest of this thesis, however, will not involve loop space. We will see a Nahm-like construction for the case of infinitely many selfdual strings, suspended between two M5-branes. This is possible since the limit taken renders the fields describing the M5-branes abelian. This avoids the problem which the rest of this thesis focuses on: What fields describe multiple M5-branes? The answer is likely to involve higher gauge theory, a categorification of gauge theory which describes the parallel transport of extended objects. Any theories which involves 3-algebras, including current M2-brane models and the Lambert-Papageorgakis M5-brane model, are examples of higher gauge theories. Recently, a class of models with N = (1, 0) supersymmetry have been found, with significant overlap with algebraic structures in higher gauge theory. This overlap suggests that the full N = (2, 0) theory could involve semistrict L∞-algebras. Finally, we will see some explicit selfdual string solutions, which may fit into these frameworks.
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Vedrashko, Alexander William. "The Alchian and Allen theorem: theory and evidence". Thesis, Montana State University, 1998. http://etd.lib.montana.edu/etd/1998/vedrashko/VedrashkoA1998.pdf.
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The Alchian and Allen theorem states that when a common per unit fee is added to the prices of high and low quality goods, the relative price of the high quality good falls, and its relative consumption increases. The theorem has been analyzed in the literature under the assumption that the prices of the goods are exogenous. This thesis presents a spatial equilibrium model that drops this restriction. The comparative statics analysis developed in this thesis does not support the theorem proposition in the general case. The theorem is then tested empirically on U.S. hard wheat exports. Transport costs, represented by ocean grain freight rates, are not found to have a significant influence on the average quality of U.S. wheat exports for the group of importing countries with a high per capita incomes that have not received U.S. export subsidies. However, transport costs are shown to be positively related with the average quality of U.S. wheat exports for the group of low-income importing countries. Additionally, it is shown that there exists an inverse relationship between the relative price of high quality wheat and the average quality of U.S. wheat exports for high-income countries.
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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem". Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.
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Sorokin, Yegor. "Probability theory, fourier transform and central limit theorem". Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1604.
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Patrascu, A. T. "The universal coefficient theorem and quantum field theory". Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1476590/.
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During the end of the 1950's Alexander Grothendieck observed the importance of the coefficient groups in cohomology. Three decades later, he presented his ``Esquisse d'un Programme" to the main french funding body. This program also included the use of different coefficient groups in the definition of various (co)homologies. His proposal was rejected. Another three decades later, in the 21st century, his research proposal is considered one of the most inspiring and important collection of ideas in pure mathematics. His ideas brought together algebraic topology, geometry, Galois theory, etc. becoming the origin for several new branches of mathematics. Today, less than one year after his death, Grothendieck is considered one of the most influential mathematicians worldwide. His ideas were important for the proofs of some of the most remarkable mathematical problems like the Weil Conjectures, Mordell Conjectures and the solution of Fermat's last theorem. Grothendieck's dessins d'enfant have been used in mathematical physics in various domains. Seiberg-Witten curves, N=1 and N=2 gauge theories and matrix models are a few examples where his insights are relevant. In this thesis I try to connect the idea of cohomology with coefficients in various sheaves to some areas of modern research in physics. The applications are manifold: the universal coefficient theorem presents connections to the topological genus expansion invented by 't Hooft and applied to quantum chromodynamics (QCD) and string theory, but also to strongly coupled electronic systems or condensed matter physics. It also appears to give a more intuitive explanation for topological recursion formulas and the holomorphic anomaly equations. The counting of BPS states may also profit from this new perspective. Indeed, the merging of cohomology classes when a change in coefficient groups is implemented may be related to the wall-crossing formulas and the phenomenon of decay or coupling of BPS states while crossing stability walls. The $Ext$ groups appearing in universal coefficient theorems may be regarded as obstructions characterizing the phenomena occurring when BPS stability walls are being crossed. Another important aspect is the existence of dualities. These are the non-perturbative analogue of symmetry transformations. Until now, they were discovered more by accident or by educated guesswork. I show in this thesis that there exists an underlying structure to the dualities, a structure that connects them the number fields used as coefficients in (co)homologies. This observation makes a nontrivial connection between number theory and physics.
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Walters, Mark Jon. "Ramsey theory, discrepancy theory and related areas". Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621647.
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Stefański, Bogdan. "String theory, dirichlet branes and K-theory". Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621023.
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Sacco, Damiano. "Aspects of F-Theory and M-Theory". Thesis, King's College London (University of London), 2017. https://kclpure.kcl.ac.uk/portal/en/theses/aspects-of-ftheory-and-mtheory(b5d27efa-8fc4-47a4-b259-a7b8dd9c218f).html.
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Non-perturbative phenomena have received much attention in string theory in the last years. M-Theory and F-Theory are the two main frameworks in which it is possible to explore such phenomena. This thesis focuses on aspects of both theories. In the first part of this thesis we study F-Theory compactifications with additional abelian gauge symmetries. This was motivated by problems affecting usual F-Theory compactifications and 4-dimensional Grand Uni ed Theories such as the presence of proton decay operators, which could in principle be resolved with additional abelian symmetries. In the F-Theory context, this translated into the novel analysis of elliptic brations with additional (two, in particular) rational sections. A systematic study of the possible degenerations of such elliptic brations through the application of Tate's algorithm was carried out and provided new insight into the phenomenology of F-Theory models with additional U(1) factors. The second part of this thesis consists of the study of some aspects of membranes in M-Theory. D-branes in string theory are well understood thanks to a perturbative definition via open strings. On the contrary, membranes and vebranes in M-Theory lack such a description and their effective theories are not as well understood. In particular the theory on parallel M5-branes, the so-called (2,0) theory, was studied in some detail. Following a number of results and dualities in lower dimensional field theories obtained in the last years starting from the (2,0) theory, the latter was compactified on a 2-dimensional sphere to obtain a 4-dimensional sigma model into the moduli space of monopoles. A supergravity background was turned on in order to preserve supersymmetry and an intermediate reduction to 5-dimensional N = 2 Super-Yang-Mills theory was used by considering the two-sphere as a circle bration over an interval. Insight into the theory on parallel M5-branes was also gained by relating it to the better known dynamics on coincident M2-branes. This followed a recent proposal for the realization of the (2,0) algebra on a non-abelian tensor multiplet through the use of 3-algebras. In this thesis we generalize this proposal and nd an algebraic structure which describes two parallel M5-branes or two parallel M2-branes depending on whether a particular abelian three-form is turned on.
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Winterhalter, Théo. "Formalisation and Meta-Theory of Type Theory". Thesis, Nantes, 2020. http://www.theses.fr/2020NANT4012.
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Dans cette thèse, je parle de la méta-théorie de la théorie des types et de la façon de la formaliser dans un assistant de preuve. Je me concentre d’abord sur une traduction conservative de la théorie des types extensionnelle vers la théorie des types intensionnelle ou faible, entièrement écrite en Coq. La première traduction consiste en une suppression de la règle de reflection de l’égalité, tandis que la deuxième traduction produit quelque chose de plus fort : la théorie des types faibles est une théorie des types sans notion de conversion. Le résultat de conservativité implique que la conversion n’augmente pas la puissance logique de la théorie des types. Ensuite, je montre ma contribution au projet MetaCoq de formalisation et de spécification de Coq au sein de Coq. En particulier, j’ai travaillé sur l’implantation d’un vérificateur de type pour Coq, en Coq. Ce vérificateur de type est prouvé correct vis à vis de la spécification et peut être extrait en code OCaml et exécuté indépendamment du vérificateur de type du noyau de Coq. Pour que cela fonctionne, nous devons nous appuyer sur la métathéorie de Coq que nous développons, en partie, dans le projet MetaCoq. Cependant, en raison des théorèmes d’incomplétude de Gödel, nous ne pouvons pas prouver la cohérence de Coq dans Coq, ce qui signifie que certaines propriétés — principalement la forte normalisation — doivent être supposées, c’est-à-dire prises comme axiomesIn this thesis, I talk about the metatheory of type theory and about how to formalise it in a proof assistant. I first focus on a conservative translation between extensional type theory and either intensional or weak type theory, entierely written in Coq. The first translation consists in a removal of the reflection of equality rule, whereas the second translation produces something stronger: weak type theory is a type theory with no notion of conversion. The conservativity result implies that conversion doesn’t increase the logical power of type theories. Then, I show my work for the Meta- Coq project of formalising and specifying Coq within Coq. In particular I worked on writing a type-checker for Coq, in Coq. This type checker is proven sound with respect to the specification and can be extracted to OCaml code and run independently of Coq’s kernel type-checker. For this to work we have to rely on the meta-theory of Coq which we develop, in part, in the MetaCoq project. However, because of Gödel’s incompleteness theorems, we cannot prove consistency of Coq within Coq, and this means that some properties— mainly strong normalisation—have to be assumed, i.e. taken as axioms
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Leclerc, Philip. "Prospect Theory Preferences in Noncooperative Game Theory". VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3522.
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The present work seeks to incorporate a popular descriptive, empirically grounded model of human preference under risk, prospect theory, into the equilibrium theory of noncooperative games. Three primary, candidate definitions are systematically identified on the basis of classical characterizations of Nash Equilibrium; in addition, three equilibrium subtypes are defined for each primary definition, in order to enable modeling of players' reference points as exogenous and fixed, slowly and myopically adaptive, highly flexible and non-myopically adaptive. Each primary equilibrium concept was analyzed both theoretically and empirically; for the theoretical analyses, prospect theory, game theory, and computational complexity theory were all summoned to analysis. In chapter 1, the reader is provided with background on each of these theoretical underpinnings of the current work, the scope of the project is described, and its conclusions briefly summarized. In chapters 2 and 3, each of the three equilibrium concepts is analyzed theoretically, with emphasis placed on issues of classical interest (e.g. existence, dominance, rationalizability) and computational complexity (i.e, assessing how difficult each concept is to apply in algorithmic practice, with particular focus on comparison to classical Nash Equilibrium). This theoretical analysis leads us to discard the first of our three equilibrium concepts as unacceptable. In chapter 4, our remaining two equilibrium concepts are compared empirically, using average-level data originally aggregated from a number of studies by Camerer and Selten and Chmura; the results suggest that PT preferences may improve on the descriptive validity of NE, and pose some interesting questions about the nature of the PT weighting function (2003, Ch. 3). Chapter 5 concludes, systematically summarizes theoretical and empirical differences and similarities between the three equilibrium concepts, and offers some thoughts on future work.
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Berg, Deborah. "Connections Between Voting Theory and Graph Theory". Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/178.
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Mathematical concepts have aided the progression of many different fields of study. Math is not only helpful in science and engineering, but also in the humanities and social sciences. Therefore, it seemed quite natural to apply my preliminary work with set intersections to voting theory, and that application has helped to focus my thesis. Rather than studying set intersections in general, I am attempting to study set intersections and what they mean in a voting situation. This can lead to better ways to model preferences and to predict which campaign platforms will be most popular. Because I feel that allowing people to only vote for one candidate results in a loss of too much information, I consider approval voting, where people can vote for as many platforms as they like.
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Bastianello, Lorenzo <1988>. "Essays on decision theory and bargaining theory". Doctoral thesis, Università Ca' Foscari Venezia, 2016. http://hdl.handle.net/10579/9391.
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This thesis is composed by three chapters that correspond to three articles.
The first two chapters deal with the theory of inter-temporal choices. A new concept, called delay aversion, is introduced and is analysed in two contexts. In the first one, I study the case of a delay averse decision maker who has preferences represented by a functional over the set of bounded, infinite streams of income. This functional may be either the Choquet integral or the MaxMin operator. Sever mathematical characterization are given. In the second framework I introduce a new topology over the set of bounded, real-valued sequences. This topology is shown to "discount" the future in a way consistent with delay aversion. Again, several mathematical properties are studied.
The third chapter focuses on the theory of bargaining. The cooperative model of bargaining proposed by Nash is studied by introducing a mediator who should make two bargainers strike an agreement. By imposing several axioms on the preferences of the mediator, I prove that she should make an offer that maximises the probability of joint acceptance. More technically, I find that she should maximise a copula. This approach allows to recover several bargaining solutions existing in the literature as specific cases.
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Braun, Volker Friedrich. "K-theory and exceptional holonomy in string theory". Doctoral thesis, [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965401650.
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Akdenizli, Dilek. "Critical Theory, Deliberative Democracy And International Relations Theory". Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12606881/index.pdf.
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In the 20th century, Critical Theory has been very influential on every discipline of social sciences including international relations. According to Critical IR Theory, traditional theories are problem solving and try to explain repetition and recurrence, rather than changehowever, the main subject matter of an IR theory should be the change itself. The idea of change is also constitutive of Habermasian political thought. Jü
rgen Habermas, as a critical theorist, has developed the model of Deliberative Democracy to provoke a change in the political life of the Western countries towards a more ethical politics. According to Habermas, such a change will eliminate the legitimacy crisis occurred in Western democracies. Therefore, Habermas aims at strengthening the moral basis of democratic understanding in order to make masses participate actively in decision making processes. According to him, rational consensus must be at the centre of democracy, and it can be reached, only if every part of the deliberation has the opportunity to express their arguments equally. Once the idea of rational consensus becomes a regulative rule of democracy, it is possible to change the nature of politics, including international politics
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Halter, Sebastian. "Inflation from field theory and string theory perspectives". Diss., Ludwig-Maximilians-Universität München, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-156269.
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Acharya, Bobby Samir. "Joyce compactifications of string theory and M theory". Thesis, Queen Mary, University of London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299930.
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Bedford, James Andrew Peter. "On perturbative field theory and twistor string theory". Thesis, Queen Mary, University of London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.479158.
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Fritz, Jan-Stefan. "Regime theory : a new theory of international institutions". Thesis, London School of Economics and Political Science (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392682.
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Knoll, Meredith Sharyn. "Rethinking the #theory' in theory of mind development". Thesis, University College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272550.
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Lake, Matthew James. "Cosmic necklaces in string theory and field theory". Thesis, Queen Mary, University of London, 2010. http://qmro.qmul.ac.uk/xmlui/handle/123456789/523.
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In this thesis we investigate astrophysical phenomena which arise in models with compact extra dimensions, focussing on the cosmological consequences of strings which wrap cycles in the internal space. Embedding our strings in the Klebanov-Strassler geometry we develop a concrete model of cosmic necklaces and investigate the formation of primordial black holes and dark matter relics from necklace collapse. Using data from the EGRET cosmic ray experiment, we place bounds on the parameters which de ne the warped deformed conifold, including the value of the warp factor and the radius of the compact space. Chapter 1 provides a brief overview, while background material is included in chapter 2, and these results are presented in chapter 3. In chapter 4 we analyse the dynamics of wound strings with angular momentum in the compact dimensions and determine the equation of motion for a self-oscillating loop. Finally, in chapter 5 we suggest a eld-theoretic dual for wound-string necklaces based on a modi cation of the standard Abelian-Higgs model. After introducing spatially-dependent couplings for the scalar and vector elds, we propose a static, non-cylindrically symmetric solution of the resulting eld equations which describes a \pinched" string with neighbouring vortex and anti-vortex regions. The similarities between pinched strings and the four-dimensional appearance of wound-string states are then examined and a correspondence between eld theory and string theory parameters is suggested. We nd that the topological winding number of the eld theory vortex may be expressed in terms of parameters which de ne the winding of the dual string around the compact space. According to this relation, the topological charge is equal to unity when the string has zero windings, and the standard Nielsen-Olesen duality is recovered in this limit. One key result of this work is an estimate of the Higgs boson mass (at critical coupling) in terms of the parameters which de ne the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.
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Letzter, Shoham. "Extremal graph theory with emphasis on Ramsey theory". Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709415.
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Feng, Bo 1971. "D-branes, gauge theory and string field theory". Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8491.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.Includes bibliographical references (p. 245-262).
In this thesis, we present several works done in last three years. They include three directions in the string theory. In the first direction, we use the brane setup to find mirror pairs of SO(n) and Sp(k) gauge groups for N = 4 three-dimensional gauge field theories. To reach this result, we analyze carefully the s-configuration and predict a nontrivial string dynamics, i.e., the splitting of branes on the orientifold planes. In the second direction, we develop the "inverse algorithm" and use it to get nontrivial world volume theories of D-branes probing more exotic singularities. In this process, we find the "toric duality" which relates different phases of D-brane probe theories. We realize later that the toric duality is an example of the more powerful Seiberg-duality so these different phases are related by the Seiberg duality. In the third direction, by using numerical calculation we get a strong evidence to support the second conjecture of Sen's three conjectures. We show that if the identity field is BRST exact state around the tachyon vacuum, the open string spectrum will decouple from the physics and leave only the closed string spectrum.
by Bo Feng.
Ph.D.
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Hamza, Taher Tawfik Ahmed. "Normalisation techniques in proof theory and category theory". Thesis, University of St Andrews, 1986. http://hdl.handle.net/10023/13371.
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The word problem for the free categories with some structure generated by a category X can be solved using proof-theoretical means. These free categories give a semantics in which derivations of GENTZEN's propositional sequent calculus can be interpreted by means of arrows of those categories. In this thesis we describe, implement and document the cut-elimination and the normalization techniques in proof theory as outlined in SZABO [1978]: we show how these are used in order to solve, mechanically, the word problem for the free categories with structure of : cartesian, bicartesian, distributive bicartesian, cartesian closed, and bicartesian closed. This implementation is extended by a procedure to interpret intuitionistic propositional sequent derivations as arrows of the above categories. Implementation of those techniques has forced us to modify the techniques in various inessential ways. The description and the representation in the syntax of our implementation of the above categories is contained in chapters 1 - 5, where each chapter describes one theory and concludes with examples of the system In use to represent concepts and solve simple word problems from category theory ( of various typos ). Appendix 1 contains some apparent printing errors we have observed in the work done by SZABO. The algorithms used in the proof of the cut-elimination theorems and normalization through chapters 1 - 5 are collected in appendices 2 - 4. Appendices 5 - 8 concern the implementation and its user manual.
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Mohamed, Adam. "Local Class Field Theory via Lubin-Tate Theory /". Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1936.
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Bulinski, Kamil. "Interactions between Ergodic Theory and Combinatorial Number Theory". Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17733.
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The seminal work of Furstenberg on his ergodic proof of Szemerédi’s Theorem gave rise to a very rich connection between Ergodic Theory and Combinatorial Number Theory (Additive Combinatorics). The former is concerned with dynamics on probability spaces, while the latter is concerned with Ramsey theoretic questions about the integers, as well as other groups. This thesis further develops this symbiosis by establishing various combinatorial results via ergodic techniques, and vice versa. Let us now briefly list some examples of such. A shorter ergodic proof of the following theorem of Magyar is given: If B Zd, where d 5, has upper Banach density at least > 0, then the set of all squared distances in B, i.e., the set fkb1 b2k2 j b1; b2 2 Bg, contains qZ>R for some integer q = q( ) > 0 and R = R(B). Our technique also gives rise to results on the abundance of many other higher order Euclidean configurations in such sets. Next, we turn to establishing analogues of this result of Magyar, where k k2 is replaced with other quadratic forms and various other algebraic functions. Such results were initially obtained by Björklund and Fish, but their techniques involved some deep measure rigidity results of Benoist-Quint. We are able to recover many of their results and prove some completely new ones (not obtainable by their techniques) in a much more self-contained way by avoiding these deep results of Benoist-Quint and using only classical tools from Ergodic Theory. Finally, we extend some recent ergodic analogues of the classical Plünnecke inequalities for sumsets obtained by Björklund-Fish and establish some estimates of the Banach density of product sets in amenable non-abelain groups. We have aimed to make this thesis accesible to readers outside of Ergodic Theory who may be primarily interested in the arithmetic and combinatorial applications.
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Corson, Samuel M. "Applications of Descriptive Set Theory in Homotopy Theory". BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2401.
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This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.
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Karch, Andreas. "Field Theory Dynamics from branes in String Theory". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 1998. http://dx.doi.org/10.18452/14371.
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Nach jahrelanger Suche hat sich bis heute Stringtheorie als einziger Kandidat einer konsistenten Quantentheorie der Gravitation herauskristallisiert. Um aus der Stringtheorie präzise Vorhersagen für unsere Niederenergiewelt zu gewinnen, ist es notwendig, das Vakuumproblem zu lösen, das heißt einen Mechanismus zu finden, der aufzeigt, in welchem Stringvakuum wir leben und warum die Natur dieses ausgewählt hat. Die Beantwortung dieser Frage benötigt nicht-perturbative Informationen.Diese wurden erst in jüngster Zeit zugänglich. Eine besondere Rolle in dieser Entwicklung spielten die sogenannten D-branes. Sie stellen mögliche nicht-perturbative Beiträge zu Stringamplituden dar. Die Identifizierung, daß D-branes einfach Objekte sind, auf denen Strings enden können, ermöglicht sie zu handhaben und zu zeigen, daß ihre Dynamik im wesentlichen durch Eichtheorien erfaßt wird. D-branes erlaubten, zahlreiche Dualit\ätssymmetrien zu etablieren, deren Haupta ussage zu sein scheint, daß alle 5 Stringtheorien sowie 11d Supergravitation nur verschiedene perturbative Limites einer fundamentalen 11d Theorie sind, T-Theorie. In dieser Arbeit habe ich mich mit einigen Anwendungen dieser Ideen beschäftigt. Die Tatsache, daß D-branes durch Super Yang-Mills Theorien beschrieben werden, erlaubt uns einen Stringhintergrund derart zu präparieren, daß wir nahezu jede Eichtheorie als relevante Niederenergiebeschreibung erhalten können. Eine besonders verbreitete Variante dieser Idee sind die sogenannten ``Hanany Witten setups'', in denen dieser Stringhintergrund nur aus flachen branes im flachen Raum besteht. Mit Hilfe dieser Technik habe ich verschiedene Dualitätssymmetrien in Feldtheorien auf Stringdualitäten zurückgeführt. Ferner ist es möglich, mit Hilfe der branes die Existenz nicht trivialer Fixpunkt Theorien in sechs Dimensionen zu beweisen und einige ihrer Eigenschaften zu analysieren. Einige dieser Fixpunkte beschreiben Phasenübergänge zwischen verschiedenen brane Hintergründen. Unter anderem läßt es sich auf diese Weise zeigen, daß es in 4 Dimensionen Übergänge zwischen chiralen und nicht chiralen Vacua gibt. Ferner wurde gezeigt, daß alle anderen Zugänge zu dem Problem, Eichtheorien in Stringtheorie einzubetten, im wesentlichen äquivalent zum HW Ansatz sind, in dem Sinn, daß die entsprechenden Stringhintergründe dual zueinander sind. Dadurch können neue Aspekte der String T-Dualität verstanden werden, so wie z.B. T-Dualitäat für brane Segmente und gebogene branes.Außerdem erlaubt uns diese Verbindung, die Phasenübergänge, die wir im HW Bild entdeckt haben, tatsächlich als Übergänge zwischen topologisch verschiedenen Stringkompaktifizierungen zu verst ehen.In this thesis I discussed several applications of the connection of non-perturbative string theory and SYM theory. In Chapter 1 I reviewed the physics of D-branes as one example of a non-perturbative effect in string theory. Their dynamics is dominated by gauge theory. This fact can be used to engineer certain string backgrounds which yield interacting SYM theories as their low-energy description. In Chapter 2 I then introduced one of the approaches in detail, the HW setup. I gave a summary of the identification of the classical gauge theory, showed how quantum effects manifest themselves in the brane picture and how to solve them. This way of embedding gauge theories into string theories has several interesting applications. These were the topic of Chapter 3. First I discussed dualities in field theory and showed how they arise as a natural consequence of string duality. As a second application I used branes to prove the existence of non-trivial fixed point theories in 6 dimensions and to study their properties. Some of these fixed points describe phase transitions between two different brane configurations. From a 4d point of view these 6d transitions can induce a chiral non-chiral transition. In Chapter 4 I discussed the relation of the HW setup with the other approaches of embedding gauge theory into string theory, especially the branes as probes approach. The different ways of embedding gauge theories in string theory are shown to be actually T-dual as string backgrounds. For one this allowed us to explore several new aspects of T-duality, like T-duality for bended branes and branes endin g on branes. In addition this relation can be used to show that the transitions found in the brane picture can as well be understood as transitions between topologically distinct compactifications of string theory. Some open problems and directions for further research were mentioned in Chapter 5.
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Apedaile, Thomas J. "Computational Topics in Lie Theory and Representation Theory". DigitalCommons@USU, 2014. https://digitalcommons.usu.edu/etd/2156.
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The computer algebra system Maple contains a basic set of commands for working with Lie algebras. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for dening multiplication in several types of Cayley algebras, Jordan algebras and Cliord algebras were created to allow users to perform a variety of calculations. Second, commands were created for calculating some basic properties of nite-dimensional representations of complex semisimple Lie algebras. These commands allow one to identify a given representation as direct sum of irreducible subrepresentations, each one identied by an invariant highest weight. Third, creating an algorithm to calculate the Lie bracket for Vinberg's symmetric construction of Freudenthal's Magic Square allowed for a uniform construction of all ve exceptional Lie algebras. Maple examples and tutorials are provided to illustrate the implementation and use of the algebras now available in Maple as well as the tools for working with Lie algebra representations.
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Foote, Richard D. L. "On KK-Theory and a Theorem in Stable Uniqueness". Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10163279.
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Starting in the 1970s, Elliot’s classification of AF -algebras and Brown-Douglas-Fillmore’s classification of essentially normal operators created an explosion in the use of topological methods in the study of C * -algebras. Kasparov’s introduction of KK-theory introduced more advanced machinery. This led to better existence and uniqueness theorems with applications in the classification program. In this thesis, I present such a uniqueness theorem with a proof as presented by Eilers-Dadarlat.
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Pilota, Evdoxia. "Extreme value thepory forvalue at risk estimation : Theory and empirical application". Thesis, University of Essex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.499763.
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Haiden, Martin. "Theta theory". Berlin [u.a.] Mouton de Gruyter, 2005. http://www.loc.gov/catdir/toc/ecip0511/2005011293.html.
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Naik, A. D. "Absolute-theory". Thesis, University of Aberdeen, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379788.
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This thesis is concerned with the project which J.N. Findlay has called absolute-theory (see his book Ascent to the Absolute London: George Allen and Unwin 1970, and his article 'Bradley's contribution to Absolute-theory' in The Philosophy of F.H.Bradley edited by Guy Stock and Anthony Manser, Oxford: Clarendon 1984). In absolute-theory one is concerned with (1) determining the abstract or formal characteristics, the form as it were, of the fundamental existent or existents on which all things depend, and (ii) evaluating the candidates that might be said to fit the abstract form. If there are a plurality of fundamental existents then the form is a universal with many instances. If there is only one fundamental existent, one primordial object, then the form itself is particular in the sense that it is not instantiable by more than one thing. The background issue is monism versus pluralism. In chapter 1 first some of the characteristics that go to make up the form are delineated. Then some candidates are briefly evaluated and rejected. Finally the kind of candidate absolute idealists offer in general is elucidated to some degree giving the authors preferred formulation. The self-differentiated Substance-Person. The rest of the thesis is concerned with elucidating this conception as a candidate and arguing for it. Through this the formal characteristics of the Absolute are also considered. The author has tried to formulate an independent and original position within the general tradition of absolute idealism. In chapter 2 the concept of substance and of ultimate substance is elucidated and argued for. In chapter 3 the substance-attribute distinction is utilized to construct an original dilemma and it is argued that the solution lies in the conception of the ultimate substance. The dilemma is this: All attributes are either essential or accidental to their substances. If interaction between substances is at the level of essential attributes loss of identity occurs. If it is at the level of accidental attributes knowledge of the real nature of other substances remains ever elusive. In chapter 4 it is argued that the ultimate substance is the source of all meaning and truth. In chapter 5 it is argued that the ultimate substance is also a self-differentiated Person. This is basically the idea that there is One Person embodied in all brain-bodies.
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Muthoo, Abhinay. "Bargaining theory". Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257214.
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Selin, Philip. "Auction Theory". Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296539.
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Lanier, Joshua. "Consumer theory". Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:8ab695ff-000e-4135-a893-83d00f5a2820.
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This thesis consists of three self-contained chapters covering topics in consumer theory. The first chapter presents an estimator for a Marshallian demand function which not only obeys all of the standard assumptions of consumer theory but will also converge to any true demand function which also obeys these standard assumptions. The second chapter explores Giffen behavior in the context of financial assets. The chapter finds that an agent with Maxmin preferences almost always displays Giffen behavior in some financial environments. Giffen behavior is also characterized for other classes of preferences. The last chapter, coauthored with one of my supervisors: John K.-H. Quah, develops a revealed preference test for weakly separable preferences in the spirit of Sydney Afriat. Unlike previous tests, ours does not impose concavity and applies to nonlinear budgets.
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An, Filip. "Auction Theory". Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-359719.
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Мельник, Ю. "Coding theory". Thesis, Видавництво СумДУ, 2006. http://essuir.sumdu.edu.ua/handle/123456789/21790.
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Дядечко, Алла Миколаївна, Алла Николаевна Дядечко, Alla Mykolaivna Diadechko e N. A. Dedik. "String theory". Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/17875.
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Novak, K. "Game theory". Thesis, Sumy State University, 2016. http://essuir.sumdu.edu.ua/handle/123456789/46882.
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Game theory is a section of applied mathematics that studies various
mathematical models of optimal decision making in conflict situations. J.
Von Neumann and O. Monhenshternom in 1944 wrote the work "Theory of
Games and Economic Behavior." From the very beginning of its
development, it was aimed at solving economic problems. Later it began to
be applied in other areas related to the conflict. Theoretical and playing
methods of optimal solutions are widely used in medicine, in economic and
social planning and forecasting, and other matters of science and
technology.Today, the game theory is widely used in various sciences such
as economic, political, computer, social, etc. Game theory attempts to
identify strategic behavior in different situations mathematically in which
success is the subject of the decision-making and depends on the moves of
other players.
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Dieterly, Andrea K. "Set Theory". Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1304689030.
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Baird, Rachel A. "String Theory". Cleveland State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=csu1273803256.
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Frere, Scot M. (Scot Martin). "Dimension Theory". Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc500690/.
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This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of covering dimension and theorems discussing the equivalence of the different dimension functions in certain topological settings. Arguments pertaining to the dimension o f Jn are also contained in Chapter IV.