Dissertations / Theses on the topic 'Fixed points of morphisms'
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Nevisi, Hossein. "Conditions on the existence of unambiguous morphisms." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/10282.
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A morphism $\sigma$ is \emph{(strongly) unambiguous} with respect to a word $\alpha$ if there is no other morphism $\tau$ that maps $\alpha$ to the same image as $\sigma$. Moreover, $\sigma$ is said to be \emph{weakly unambiguous} with respect to a word $\alpha$ if $\sigma$ is the only \emph{nonerasing} morphism that can map $\alpha$ to $\sigma(\alpha)$, i.\,e., there does not exist any other nonerasing morphism $\tau$ satisfying $\tau(\alpha) = \sigma(\alpha)$. In the first main part of the present thesis, we wish to characterise those words with respect to which there exists a weakly unambiguous \emph{length-increasing} morphism that maps a word to an image that is strictly longer than the word. Our main result is a compact characterisation that holds for all morphisms with ternary or larger target alphabets. We also comprehensively describe those words that have a weakly unambiguous length-increasing morphism with a unary target alphabet, but we have to leave the problem open for binary alphabets, where we can merely give some non-characteristic conditions. \par The second main part of the present thesis studies the question of whether, for any given word, there exists a strongly unambiguous \emph{1-uniform} morphism, i.\,e., a morphism that maps every letter in the word to an image of length $1$. This problem shows some connections to previous research on \emph{fixed points} of nontrivial morphisms, i.\,e., those words $\alpha$ for which there is a morphism $\phi$ satisfying $\phi(\alpha) = \alpha$ and, for a symbol $x$ in $\alpha$, $\phi(x) \neq x$. Therefore, we can expand our examination of the existence of unambiguous morphisms to a discussion of the question of whether we can reduce the number of different symbols in a word that is not a fixed point such that the resulting word is again not a fixed point. This problem is quite similar to the setting of Billaud's Conjecture, the correctness of which we prove for a special case.
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Hendtlass, Matthew. "Constructing fixed points and economic equilibria." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/4973/.
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Constructive mathematics is mathematics with intuitionistic logic (together with some appropriate, predicative, foundation)-it is often crudely characterised as mathematics without the law of excluded middle. The intuitionistic interpretation of the connectives and quantifiers ensure that constructive proofs contain an inherent algorithm which realises the computational content of the result it proves, and, in contrast to results from computable mathematics, these inherent algorithms come with fixed rates of convergence. The value of a constructive proof lies in the vast array of models for constructive mathematics. Realizability models and the interpretation of constructive ZF set theory into Martin Löf type theory allows one to view constructive mathematics as a high level programing language, and programs have been extracted and implemented from constructive proofs. Other models, including topological forcing models, of constructive set theory can be used to prove metamathematical results, for example, guaranteeing the (local) continuity of functions or algorithms. In this thesis we have highlighted any use of choice principles, and those results which do not require any choice, in particular, are valid in any topos. This thesis looks at what can and cannot be done in the study of the fundamental fixed point theorems from analysis, and gives some applications to mathematical economics where value is given to computability.
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Panicker, Rekha Manoj. "Some general convergence theorems on fixed points." Thesis, Rhodes University, 2014. http://hdl.handle.net/10962/d1013112.
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In this thesis, we first obtain coincidence and common fixed point theorems for a pair of generalized non-expansive type mappings in a normed space. Then we discuss two types of convergence theorems, namely, the convergence of Mann iteration procedures and the convergence and stability of fixed points. In addition, we discuss the viscosity approximations generated by (ψ ,ϕ)-weakly contractive mappings and a sequence of non-expansive mappings and then establish Browder and Halpern type convergence theorems on Banach spaces. With regard to iteration procedures, we obtain a result on the convergence of Mann iteration for generalized non-expansive type mappings in a Banach space which satisfies Opial's condition. And, in the case of stability of fixed points, we obtain a number of stability results for the sequence of (ψ,ϕ)- weakly contractive mappings and the sequence of their corresponding fixed points in metric and 2-metric spaces. We also present a generalization of Fraser and Nadler type stability theorems in 2-metric spaces involving a sequence of metrics.
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Morris, David. "Extending local analytic conjugacies between parabolic fixed points." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/102605/.
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The focus of this thesis is a study of the extension properties of local analytic conjugacies between simple parabolic fixed points. Any given conjugacy itself will generally not have an extension to the immediate basin. However, we show that if both maps belong to a suitable class (which includes polynomial-like maps and rational maps with a simply connected parabolic basin) then for all n large enough g on o X does have an analytic extension to the immediate parabolic basin. We begin by studying qualitative models for the dynamics near a parabolic fixed point, leading us to the Parabolic Flower Theorem. We then construct Fatou coordinates, which conjugate f to the unit translation, and study extension and properties of these maps. By restricting ourselves to the case when the restriction of f to its parabolic basin is a proper map with finitely many critical points we are able to study covering properties of these extended Fatou coordinates. We also introduce the horn map and lifted horn maps and show that the former is a complete invariant of the local analytic conjugacy class. Working from the covering properties of the horn map, we develop an intuition for how critical orbits of two maps f and g with locally conjugate simple parabolic fixed points should be related. In our main theorem, Theorem 3.1.10, we show that if both maps have a proper parabolic basin and is a local analytic conjugacy from (f; z0) to (g; w0) then for all n large enough, the map g on o X has an analytic extension along any curve starting in a region near z0 contained in the basin of z0. Under the additional assumption that the immediate basin is simply connected we can then conclude that the map Xn := g on o X has an analytic extension to a semi-conjugacy between the immediate basins whenever n is large enough.
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Jeganathan, P. "Fixed points for nonexpansive mappings in Banach spaces." Master's thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/17067.
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Lanzagorta, Marco. "Infra-red fixed points in supersymmetric Grand Unified theories." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318836.
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Simms, R. "Exploring higher dimensional quantum field theories through fixed points." Thesis, University of Liverpool, 2018. http://livrepository.liverpool.ac.uk/3028491/.
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Renormalization was popularised in the 1940s following the appearance of non- sensical infinities in the calculation of the self-energy of the electron. Notably this led to Quantum Electrodynamics becoming a fully renormalizable quantum field theory. One useful tool that emerges from the technical aspects of renormal- ization is the Renormalization Group. In particular, the β-function defines the variation of the coupling constants with energy. The vanishing of the β-function at a particular value of the coupling is known as a fixed point, the location of which can be found using perturbation theory. Properties of quantum field the- ories such as ultraviolet behaviour can be studied using these fixed points. The calculation of two different types of fixed points forms the spine of this thesis. In Part I the d-dimensional Wilson-Fisher fixed point is used to connect scalar quantum field theories in different space-time dimensions. Specifically we look at dimensions greater than four and explore the property of universality through the Vasil'ev large N expansion. Different universality classes are examined, the first contains φ4 theory with O(N) symmetry while another incorporates O(N)×O(m) Landau-Ginzburg-Wilson theory. In the latter we perform a full fixed point sta- bility analysis and conformal window search which determines where conformal symmetry is present. Part I develops techniques that may later be applicable to calculations involving beyond the Standard Model physics including asymptotic safety, quantum gravity and emergent symmetries. Part II focuses on the non-trivial Banks-Zaks fixed point of four dimensional Quantum Chromodynamics. Using a variety of colour groups and representations we calculate the location of the fixed point and corresponding critical exponents to pinpoint exactly where the true value of the conformal window lies. Additionally a number of different renormalization schemes are used, including the momentum subtraction (MOM) and interpolating momentum subtraction (iMOM) schemes. This allows us to study where in the conformal window scheme dependence is most apparent. Both the Landau gauge and maximal abelian gauge are utilized to extend the analysis. Throughout this thesis we compare and contrast perturbative results with non-perturbative calculations such as those performed in lattice.
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Kretz, Mathis. "Proof-theoretic aspects of modal logic with fixed points /." Bern : [s.n.], 2006. http://www.zb.unibe.ch/download/eldiss/06kretz_m.pdf.
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Wimmer, Christian [Verfasser]. "Rational global homotopy theory and geometric fixed points / Christian Wimmer." Bonn : Universitäts- und Landesbibliothek Bonn, 2017. http://d-nb.info/1149744863/34.
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Doumane, Amina. "On the infinitary proof theory of logics with fixed points." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC123/document.
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Cette thèse traite de la theorie de la preuve pour les logiques a points fixes, telles que le μ-calcul, lalogique lineaire a points fixes, etc. ces logiques sont souvent munies de systèmes de preuves finitairesavec des règles d’induction à la Park. Il existe néanmoins d’autres sytèmes de preuves pour leslogiques à points fixes, qui reposent sur la notion de preuve infinitaire, mais qui sont beaucoupmoins developpés dans la litterature. L’objectif de cette thèse est de pallier à cette lacune dansl’état de l’art, en developpant la théorie de la preuve infnitaire pour les logiques a points fixes,avec deux domaines d’application en vue: les langages de programmation avec types de données(co)inductifs et la vérification des systèmes réactifs.Cette thèse contient trois partie. Dans la première, on rappelle les deux principales approchespour obtenir des systèmes de preuves pour les logiques à points fixes: les systèmes finitaires avecrègle explicite d’induction et les systèmes finitaires, puis on montre comment les deux approchesse relient. Dans la deuxième partie, on argumente que les preuves infinitaires ont effectivement unréel statut preuve-theorique, en montrant que la logique lineaire additive multiplicative avec pointsfixes admet les propriétés d’élimination des coupures et de focalisation. Dans la troisième partie,on utilise nos developpements sur les preuves infinitaires pour monter de manière constructive lacomplétude du μ-calcul lineaire relativement à l’axiomatisation de KozenThe subject of this thesis is the proof theory of logics with fixed points, such as the μ-calculus,linear-logic with fixed points, etc. These logics are usually equipped with finitary deductive systemsthat rely on Park’s rules for induction. other proof systems for these logics exist, which relyon infinitary proofs, but they are much less developped. This thesis contributes to reduce thisdeficiency by developing the infinitary proof-theory of logics with fixed points, with two domainsof application in mind: programming languages with (co)inductive data types and verification ofreactive systems.This thesis contains three parts. In the first part, we recall the two main approaches to theproof theory for logics with fixed points: the finitary and the infinitary one, then we show theirrelationships. In the second part, we argue that infinitary proofs have a true proof-theoreticalstatus by showing that the multiplicative additive linear-logic with fixed points admits focalizationand cut-elimination. In the third part, we apply our proof-theoretical investigations to obtain aconstructive proof of completeness for the linear-time μ-calculus w.r.t. Kozen’s axiomatization
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Matevosyan, Norayr. "Tangential Touch Between Free And Fixed Boundaries." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3559.
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Okuyama, Yusuke. "Non-linearizability of n-subhyperbolic polynomials at irrationally indifferent fixed points." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150899.
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Qi, Xiaomin. "Fixed points, fractals, iterated function systems and generalized support vector machines." Licentiate thesis, Mälardalens högskola, Utbildningsvetenskap och Matematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-33511.
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In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established.FUSION
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Stofile, Simfumene. "Fixed points of single-valued and multi-valued mappings with applications." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002960.
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The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.
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Johnston, Kevin Gregory. "Periodic Points and Surfaces Given by Trace Maps." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5985.
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In this thesis, we consider the properties of diffeomorphisms of R3 called trace maps. We begin by introducing the definition of the trace map. The group B3 acts by trace maps on R3. The first two chapters deal with the action of a specific element of B3,called αn. In particular, we study the fixed points of αn lying on a topological subspace contained in R3, called T . We investigate the duality of the fixed points of the action ofαn, which will be defined later in the thesis.Chapter 3 involves the study of the fixed points of an element called γnm, and it generalizes the results of chapter 2. Chapter 4 involves a study of the period two points of γnm. Chapters 5-8 deal with surfaces and curves induced by trace maps, in a manner described in chapter 5. Trace maps define surfaces, and we study the intersection of those surfaces. In particular, we classify each such possible intersection.
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Martino, Armando. "On automorphisms of free groups and free products and their fixed points." Thesis, Queen Mary, University of London, 1998. http://qmro.qmul.ac.uk/xmlui/handle/123456789/25565.
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Free group outer automorphisms were shown by Bestvina and Randell to have fixed subgroups whose rank is bounded in terms of the rank of the underlying group. We consider the case where this upper bound is achieved and obtain combinatorial results about such outer automorphisms thus extending the work of Collins and Turner. We go on to show that such automorphisms can be represented by certain graph of group isomorphisms called Dehn Twists and also solve the conjuagacy problem in a restricted case, thus reproducing the work of Cohen and Lustig, but with different methods. We rely heavily on the relative train tracks of Bestvina and Randell and in fact go on to use an analogue of these for free product automorphisms developed by Collins and Turner. We prove an index theorem for such automorphisms which counts not only the group elements which are fixed but also the points which are fixed at infinity - the infinite reduced words. Two applications of this theorem are considered, first to irreducible free group automorphisms and then to the action of an automorphism on the boundary of a hyperbolic group. We reduce the problem of counting the number of points fixed on the. boundary to the case where the hyperbolic group is indecomposable and provide an easy application to virtually free groups.
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Prellberg, Thomas. "Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39862.
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Nel-Sakharova, Natasha. "Development of high temperature fixed points for application in radiometry and thermometry." Diss., University of Pretoria, 2015. http://hdl.handle.net/2263/53540.
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Metrology is the science of measurement. It involves the formulation of the theoretical principles
related to the definition of the International System of Units (Système International d Unités, SI)
and the development of the technology for realising these units in practise. Reliable measurement
is important all areas of human activity. Decisions are based on measurement results. Incorrect
measurement results can lead to incorrect decisions, which may have significant health, economic
or environmental consequences.
Applications of sources of optical radiation are wide-ranging, including: medical treatment,
diagnosis and sterilisation; quality control in production processes; stimulation of plant growth in
agriculture; lighting and signalling for transport; interior and exterior lighting for buildings; solar
power generation; and earth observation. The spectral power distribution of a source must often be
known in order to ensure that the selected radiation source (and detector) is suitable for the intended
purpose and to optimise process efficiency. Sometimes spectral measurements are required to
demonstrate compliance with regulatory requirements (such as Occupational Health and Safety,
Aviation Authority regulations, Emergency Lighting and Road Lighting regulations). Spectral
measurements in the ultraviolet region are especially important due to its associated biological
hazard.
The accuracy of a measurement result can only be known if it is traceable to a national measurement
standard. The National Metrology Institute of South Africa (NMISA) realises and maintains
the national measurement standards for South Africa. Sources of optical radiation can be calibrated
in terms of spectral irradiance over the wavelength range 250 nm to 1 300 nm. The NMISA
currently imports traceability for spectral irradiance by sending primary standard lamps to another
National Metrology Institute (NMI) for calibration. The uncertainties of calibration are 4 % to 8 %
(k = 2) over the wavelength range of 400 nm to 1 500 nm. A primary spectral irradiance facility
is being developed, which will allow the NMISA to realise the scale independently, eliminating
the need to import traceability. Through developing this facility, the NMISA aims to achieve an uncertainty of < 1 % over the visible wavelengths.
Many NMIs realise the spectral irradiance scale by obtaining traceability from a primary standard
cryogenic radiometer through calibrated filter radiometers. The filter radiometers are used to
determine the temperature of a high temperature black body functioning as a reference source,
which spectral radiance can be determined from Planck s equation. The uncertainty of the temperature
measurement makes the most significant contribution to the uncertainty of realising the
spectral irradiance scale. High temperature fixed points, above the copper point, can be used to improve
these uncertainties. After more than ten years of research, results obtained on metal-carbon
eutectic fixed points by several NMIs, showed that these novel high temperature fixed points could
lead to significant improvements in high temperature metrology and could be considered as potential
fixed points in a future International Temperature Scale.
This dissertation describes the development and characterisation of high temperature metalcarbon
fixed points at NMISA. It is demonstrated that these fixed points can be utilised as reproducible,
stable reference standards for temperatures above the copper point. The melt temperature
of Re-C cells was repeatable within 60 mK, which is equal to a relative spectral radiance value
of 0,02 % at 650 nm. The melt temperature of the d(MoC)-C cell was repeatable within 100 mK,
which is equal to a relative spectral radiance value of 0,03 % at 650 nm. Without implementing
eutectics, NMIs typically achieve a best measurement capability of 3 K (k = 2) at 2 800 K, which
contributes approximately 1 % to the overall spectral radiance measurement uncertainty. By using
eutectics the reproducibility of spectroradiometric scales can be improved by a factor of 10.
The NMISA result for Re-C (2 747,51 K ± 2,43 K, (k = 2)) is consistent with international
values and agrees with the preliminary consensus value (2 747,35 K ± 1 K, (k = 2)) within the
stated uncertainties. Only one published result for d(MoC)-C eutectics could be found, which
was by NMIJ (Japanese NMI). The NMISA result for d(MoC)-C (2 856,76 K ± 2,89 K, (k = 2))
corresponds with that published by NMIJ (2 856 K ± 4 K, (k = 2)) and compares well with the
result of measurements performed at VNIIOFI (Russian NMI) (2 856,40 K ± 2,0 K, (k = 2)) on
this particular cell. As far as can be ascertained, the most comprehensive study of d(MoC)-C was
done by the NMISA.
Once internationally agreed to melt temperatures for a selected set of high temperature eutectics
are approved and incorporated into an updated mise en pratique for the definition of the
kelvin, the NMISA could assign the international consensus value to its Re-C cells and re-realise
its high temperature scale from 961,78 ºC (the silver freeze point) up to 2 474 ºC (or higher) and
immediately, in retrospect, realise the substantially reduced uncertainty of 1 % (k = 2).Dissertation (MSc)--University of Pretoria, 2015.
Physics
MSc
Unrestricted
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CARNEVALE, JOAO MIRANDA. "GROUPS OF HOMEOMORPHISMS OF THE LINE WITH A FINITE NUMBER OF FIXED POINTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36893@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTITUIÇÕES COMUNITÁRIAS DE ENSINO PARTICULARES
Temos como objetivo principal classificar, a menos de semi-conjugação, os grupos de homeomorfismos crescentes da reta, com no máximo N pontos fixos. Começando pelos casos já classificados, N igual a 0 pelo Teorema de Holder e N igual a 1 pelo Teorema de Solodov, nosso próximo passo será classificar o caso N igual a 2. Para isso, iremos introduzir a noção de Abertura de Órbita como uma semi-conjugação dos grupos de homeomorfismos.
We have as main objective to classify, by semi-conjugation, the groups of increasing homeomorphisms of the line, with at most N fixed points. Starting with the cases already classified, N equal to 0 by Holder s Theorem and N equal to 1 by Solodov s Theorem, our next step will be to classify the case N equal to 2. For this, we will introduce the notion of Orbital Opening as a semiconjugation of the groups of homeomorphisms.
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Kalghatgi, Roshan Satish. "Reconstruction techniques for fixed 3-D lines and fixed 3-D points using the relative pose of one or two cameras." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/43590.
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In general, stereovision can be defined as a two part problem. The first is the correspondence problem. This involves determining the image point in each image of a set of images that correspond to the same physical point P. We will call this set of image points, N. The second problem is the reconstruction problem. Once a set of image points, N, that correspond to point P has been determined, N is then used to extract three dimensional information about point P.
This master's thesis presents three novel solutions to the reconstruction problem. Two of the techniques presented are for detecting the location of a 3-D point and one for detecting a line expressed in a three dimensional coordinate system. These techniques are tested and validated using a unique 3-D finger detection algorithm. The techniques presented are unique because of their simplicity and because they do not require the cameras to be placed in specific locations, orientations or have specific alignments. On the contrary, it will be shown that the techniques presented in this thesis allow the two cameras used to assume almost any relative pose provided that the object of interest is within their field of view.
The relative pose of the cameras at a given instant in time, along with basic equations from the perspective image model are used to form a system of equations that when solved, reveal the 3-D coordinates of a particular fixed point of interest or the three dimensional equation of a fixed line of interest. Finally, it will be shown that a single moving camera can successfully perform the same line and point detection accomplished by two cameras by altering the pose of the camera.
The results presented in this work are beneficial to any typical stereovision application because of the computational ease in comparison to other point and line reconstruction techniques. But more importantly, this work allows for a single moving camera to perceive three-dimensional position information, which effectively removes the two camera constraint for a stereo vision system. When used with other monocular cues such as texture or color, the work presented in this thesis could be as accurate as binocular stereo vision at interpreting three dimensional information. Thus, this work could potentially increase the three dimensional perception of a robot that normally uses one camera, such as an eye-in-hand robot or a snake like robot.
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Farmer, Matthew Ray. "Applications in Fixed Point Theory." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4971/.
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Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
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Ersoy, Kıvanç [Verfasser]. "Centralizers and Fixed Points of Automorphisms in Finite and Locally Finite Groups / Kıvanç Ersoy." Berlin : Freie Universität Berlin, 2020. http://nbn-resolving.de/urn:nbn:de:kobv:188-refubium-26475-9.
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Nisbet, Kenneth Charles. "Dynamics of mappings of the plane and of the circle." Thesis, University of Edinburgh, 1989. http://hdl.handle.net/1842/15533.
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Skjelnes, Roy Mikael. "On Hilbert schemes parameterizing points on the affine line having support in a fixed subset." Doctoral thesis, KTH, Matematik, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-2935.
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Garcia, Ignacio de Mateo. "Iterative matrix-free computation of Hopf bifurcations as Neimark-Sacker points of fixed point iterations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://dx.doi.org/10.18452/16478.
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Klassische Methoden für die direkte Berechnung von Hopf Punkten und andere Singularitaten basieren auf der Auswertung und Faktorisierung der Jakobimatrix. Dieses stellt ein Hindernis dar, wenn die Dimensionen des zugrundeliegenden Problems gross genug ist, was oft bei Partiellen Diferentialgleichungen der Fall ist. Die betrachteten Systeme haben die allgemeine Darstellung f ( x(t), α) für t grösser als 0, wobei x die Zustandsvariable, α ein beliebiger Parameter ist und f glatt in Bezug auf x und α ist. In der vorliegenden Arbeit wird ein Matrixfreies Schema entwicklet und untersucht, dass ausschliesslich aus Produkten aus Jakobimatrizen und Vektoren besteht, zusammen mit der Auswertung anderer Ableitungsvektoren erster und zweiter Ordnung. Hiermit wird der Grenzwert des Parameters α, der zuständig ist für das Verlieren der Stabilität des Systems, am Hopfpunkt bestimmt. In dieser Arbeit wird ein Gleichungssystem zur iterativen Berechnung des Hopfpunktes aufgestellt. Das System wird mit einer skalaren Testfunktion φ, die aus einer Projektion des kritischen Eigenraums bestimmt ist, ergänzt. Da das System f aus einer räumlichen Diskretisierung eines Systems Partieller Differentialgleichungen entstanden ist, wird auch in dieser Arbeit die Berechung des Fehlers, der bei der Diskretisierung unvermeidbar ist, dargestellt und untersucht. Zur Bestimmung der Hopf-Bedingungen wird ein einzelner Parameter gesteuert. Dieser Parameter wird unabhängig oder zusammen mit dem Zustandsvektor in einem gedämpften Iterationsschritt neu berechnet. Der entworfene Algorithmus wird für das FitzHugh-Nagumo Model erprobt. In der vorliegenden Arbeit wird gezeigt, wie für einen kritischen Strom, das Membranpotential eine fortschreitende Welle darstellt.Classical methods for the direct computation of Hopf bifurcation points and other singularities rely on the evaluation and factorization of Jacobian matrices. In view of large scale problems arising from PDE discretization systems of the form f( x (t), α ), for t bigger than 0, where x are the state variables, α are certain parameters and f is smooth with respect to x and α, a matrix-free scheme is developed based exclusively on Jacobian-vector products and other first and second derivative vectors to obtain the critical parameter α causing the loss of stability at the Hopf point. In the present work, a system of equations is defined to locate Hopf points, iteratively, extending the system equations with a scalar test function φ, based on a projection of the eigenspaces. Since the system f arises from a spatial discretization of an original set of PDEs, an error correction considering the different discretization procedures is presented. To satisfy the Hopf conditions a single parameter is adjusted independently or simultaneously with the state vector in a deflated iteration step, reaching herewith both: locating the critical parameter and accelerating the convergence rate of the system. As a practical experiment, the algorithm is presented for the Hopf point of a brain cell represented by the FitzHugh-Nagumo model. It will be shown how for a critical current, the membrane potential will present a travelling wave typical of an oscillatory behaviour.
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Nowak, Boris [Verfasser], and Thomas [Akademischer Betreuer] Gasenzer. "Non-thermal fixed points and superfluid turbulence in ultracold quantum gases / Boris Nowak ; Betreuer: Thomas Gasenzer." Heidelberg : Universitätsbibliothek Heidelberg, 2012. http://d-nb.info/1177040301/34.
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Tan, Wah Lay, Lok-tin Wong, 陳華麗, and 黃洛天. "A systematic review of post-extractional alveolar hard and soft tissue dimensional changes in humans : comparison of studies with non-fixed or fixed reference points." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48395456.
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Background: Removal of teeth results in both horizontal and vertical changes of hard and soft tissue dimensions. The magnitude of these changes is important for decision-making and comprehensive treatment planning, with provisions for possible solutions to expected complications during prosthetic rehabilitation.
Objectives: to review all English dental literature to assess the magnitude of dimensional changes of both the hard and soft tissues of the alveolar ridge up to 12 months following tooth extraction in humans.
Materials and methods: An electronic MEDLINE and CENTRAL search complemented by manual searching was conducted to identify randomised controlled clinical trials and prospective cohort studies on hard and soft tissue dimensional changes after tooth extraction. Only studies reporting on undisturbed post-extraction dimensional changes relative to a fixed reference point over a clearly stated time period were included. Assessment of the identified studies and data extraction was performed independently by two reviewers. Data collected were reported by descriptive methods. Weighted means and percentages of the dimensional changes over time were calculated where appropriate.
Results: The search provided 3954 titles and 238 abstracts. Full text analysis was performed for 104 articles resulting in 20 studies that met the inclusion criteria. In human hard tissue, horizontal dimensional reduction (3.79 ± 0.23 mm) was more than vertical reduction (1.24 ± 0.11 mm on buccal, 0.84 ± 0.62 mm on mesial and 0.80 ± 0.71 mm on distal sites) at 6 months. Percentage vertical dimensional change was 11-22 % at 6 months. Percentage horizontal dimensional change was 32% at 3 months, and 29-63% at 6-7 months. Soft tissue changes demonstrated 0.4-0.5 mm gain of thickness at 6 months on the buccal and lingual aspects. Horizontal dimensional changes of hard and soft tissue (loss of 0.1 mm to 6.1 mm) was more substantial than vertical change (loss 0.9 mm to gain 0.4mm) during observation periods of up to 12 months, when study casts were utilised as a means of documenting the changes.
Conclusions: Human re-entry studies showed horizontal bone loss of 29-63% and vertical bone loss of 11-22% after 6 months following tooth extraction. These studies demonstrated rapid reductions in the first 3-6 months that was followed by gradual reductions in dimensions thereafter.published_or_final_version
Dental Surgery
Master
Master of Dental Surgery
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Sauma, Perez Tania Javiera. "An experimental study on the motion and fixed points of a light sphere in a Stokes' flow." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/an-experimental-study-on-the-motion-and-fixed-points-of-a-light-sphere-in-a-stokes-flow(b91c1a33-6cd4-4d64-a750-5e9ea3c3be76).html.
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A single light sphere is placed inside of a drum completely filled with a viscous fluid. the drum rotates perpendicular to gravity such that the Reynolds number remains small. In this flow configuration there is a wide range of behaviours. We have measured eccentric fixed points, circular orbits and asymmetric orbits by the walls of the drum. A full description of these phenomena is given as a function of the size of the sphere. We have also studied the case of a porous sphere and compared it the solid case. Finally we have studied the effect of roughness on this system.
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Chantesana, Isara [Verfasser], and Thomas [Akademischer Betreuer] Gasenzer. "Strong Wave Turbulence and Non-Thermal Fixed Points in a Kinetic Theory / Isara Chantesana ; Betreuer: Thomas Gasenzer." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177691302/34.
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Ostapyuk, Olena. "Backward iteration in the unit ball." Diss., Kansas State University, 2011. http://hdl.handle.net/2097/11931.
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Doctor of PhilosophyDepartment of Mathematics
Pietro Poggi-Corradini
We consider iteration of an analytic self-map f of the unit ball in the N-dimensional complex space C[superscript]N. Many facts were established about such maps and their dynamics in the 1-dimensional case (i.e. for self-maps of the unit disk), and we generalize some of them in higher dimensions. In one dimension, the classical Denjoy-Wolff theorem states the convergence of forward iterates to a unique attracting fixed point, while backward iterates have much more complicated nature. However, under additional conditions (when the hyperbolic distance between two consecutive points stays bounded), backward iteration sequence converges to a point on the boundary of the unit disk, which happens to be a fixed point with multiplier greater than or equal to 1. In this paper, we explore backward-iteration sequences in higher dimension. Our main result shows that in the case when f is hyperbolic or elliptic, such sequences with bounded hyperbolic step converge to a point on the boundary, other than the Denjoy-Wolff (attracting) point. These points are called boundary repelling fixed points (BRFPs) and possess several nice properties. In particular, in the case when such points are isolated from other BRFPs, they are completely characterized as limits of backward iteration sequences. Similarly to classical results, it is also possible to construct a (semi) conjugation to an automorphism of the unit ball. However, unlike in the 1-dimensional case, not all BRFPs are isolated, and we present several counterexamples to show that. We conclude with some results in the parabolic case.
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Vargas, Walter Teofilo Huaraca. ""Sobre a existência de pontos periódicos para homeomorfismos do anel fechado"." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-28082006-151440/.
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O conhecido Teorema de Poincaré afirma: O número de rotação de homeomorfismo do círculo S^1 que preserva orientação é racional se, e somente se, o homeomorfismo possui um ponto periódico cujo período é igual ao denominador de tal racional. Na presente dissertação estudamos resultados análogos, ao resultado acima mencionado, para homeomorfismos do anel A=S^1 x I homotópicos à identidade. Mais precisamente, estudaremos o famoso Teorema de Poincaré - Birkhoff e algumas versões devidas a J. Franks. Isto será feito impondo algumas condições no conjunto de rotação, o qual é uma generalização do número de rotação para homeomorfismos do círculo.The well known Poincaré's Theorem state: The rotation number of an orientation preserving circle homeomorphism is rational if, only if, the homeomorphism has a periodic point of period equal to denominator of the rational. In this monograph we study results analogous, to the result above mentioned, for homeomorphisms of A=S^1 x I homotophics to the identity. More precisely, we study the famous Poincaré - Birkhoff Theorem and some versions obtained by J. Franks. This it will be done imposing some conditions in the rotation set, which is generalization of the rotation number for circle homeomorphisms.
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Moch, Kevin [Verfasser], Gudrun [Akademischer Betreuer] Hiller, and Daniel F. [Gutachter] Litim. "Fixed points in supersymmetric extensions of the Standard Model / Kevin Moch ; Gutachter: Daniel F. Litim ; Betreuer: Gudrun Hiller." Dortmund : Universitätsbibliothek Dortmund, 2020. http://d-nb.info/1217843574/34.
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Masters, Anthony. "Rearrangements and vortices." Thesis, University of Bath, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619240.
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Rearrangements are two measurable real-valued functions that have equal measure of pre-images of upper level sets. In this thesis, I will investigate several matters and problems relating to rearrangements: the relationship between assumptions on the measure space and desirable properties of the set of rearrangements, and the validity of rearrangement inequalities; generalising the Mountain Pass Lemma over rearrangements; and applying topological degree theory to boundary value problems involving rearrangements. From suppositions on the measure space, such as the measure space having finite measure and no atoms, it can proved that the set of rearrangements is contractible and locally contractible. The Mountain Pass Lemma over rearrangements can be generalised, so instead of considering continuous paths from the closed unit interval to the set of rearrangements; it will consider the continuous functions from the closed unit disc into the set of rearrangements. Topological degree theory is used to associate admissible triples of functions, sets and points with integers. These methods will be applied to a boundary value problem involving rearrangements, where the domain is almost equal to the union of balls, which has been studied using variational methods, providing new multiplicity results. The minimum number of solutions to this boundary value problem is found to be related exponentially to the number of balls contained in the domain.
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Born, Stefan [Verfasser]. "Critical point theory for symmetries with fixed points = Theorie kritischer Punkte für Symmetrien mit Fixpunkten [[Elektronische Ressource]] / Stefan Born." Gießen : Universitätsbibliothek, 2011. http://d-nb.info/1063111242/34.
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Bond, Andrew David. "Weakly coupled fixed points and interacting ultraviolet completions of vanilla quantum field theories, or, Better asymptotically safe than asymptotically sorry." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/80674/.
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The renormalisation group is a crucial tool for understanding scale-dependent quantum field theories. Renormalisation group fixed points correspond to theories where scale invariance is restored at the quantum level, and may provide high- or low-energy limits for more general quantum field theories. In particular, those reached in the ultraviolet allow theories to be defined microscopically, a scenario known as asymptotic safety. In this work I investigate fixed points of conventional four-dimensional, at-space, perturbatively renormalisable, local quantum field theories. Focusing on weakly interacting fixed points the problem becomes amenable to perturbation theory. The approach is twofold: on the one hand to understand general conditions for the existence of such fixed points, and on the other to construct theories which introduce new features compared to previous examples. To understand perturbative fixed points, general calculations for theories of this type are exploited. It is established, for gauge theories, interacting fixed points may be nonzero in gauge couplings alone, or in gauge and Yukawa couplings. Deriving novel group theory bounds it is established that only the latter may possibly be ultraviolet. Additionally it is shown that theories without gauge interactions cannot possess weakly coupled fixed points, and the connexion between this fact and the impossibility of such theories being asymptotically free is highlighted. Two explicit families of examples are presented: a theory with semisimple gauge group is analysed in detail, containing many new fixed points, a rich phase structure, and asymptotically safe regions of parameter space, and a separate supersymmetric model with an ultraviolet fixed point, providing the first known explicit example of an asymptotically safe supersymmetric gauge theory.
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Keawprasert, Thada [Verfasser], and Stephan [Akademischer Betreuer] Völker. "Monochromator-based absolute calibration of radiation thermometers for thermodynamic temperature measurements of high-temperature fixed-points / Thada Keawprasert. Betreuer: Stephan Völker." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2011. http://d-nb.info/1014971705/34.
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Malik, Zohaib. "Modelling the freezing behaviour of ITS-90 metal fixed points for better understanding of the influence of impurities and thermal effects." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/10225.
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The methods currently used by metrologists for estimating the influence of impurities in metal fixed points require accurate knowledge of the concentrations of impurities present and of liquidus slopes of binary systems. In this thesis, two alternative methods are presented that can estimate the influence of impurities without requiring any knowledge of the impurities. Both methods are based on Scheil’s solidification model. By using a numerical solidification model it is shown that the freezing behaviour of a fixed point cell can approximate to Scheil’s model when the freezing time is greater than x2 / D, where x is the thickness of the ingot and D is the diffusion coefficient of impurities in the liquid. The first method uses the gradient of a freezing curve at about 0.5 fraction solid, and is able to predict the influence of impurities with a maximum uncertainty of around 25%. This is assuming that all the important impurities have distribution coefficients much lower than 1, which is often the case in practice. By applying some modifications to this method, it is possible to determine whether or not the distribution coefficients of the dominant impurities lie below or above 1. The second method involves numerically best fitting Scheil’s equation to a freezing curve. This method works for materials with multiple impurities, but problems arise when it is applied to an experimental freezing curve due to distortion in the freeze plateau. This is thought to be caused by the thermal effects arising from the non-uniform thermal conditions under which the fixed point is realised. It is experimentally and numerically demonstrated that the thermal uniformity of the three-zone furnace is improved by separating (thermally isolating) the heating zones. By modelling the freezing behaviour of a silver cell in the three-zone furnace it is shown that (a) increasing the freeze undercooling increases the influence of the thermal effects and adversely affects the shape of the freeze plateau, and (b) making the temperature at the base of the cell higher than that at the top reduces the influence of the thermal effects and improves the shape of the freeze plateau.
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Schmied, Christian-Marcel [Verfasser], and Thomas [Akademischer Betreuer] Gasenzer. "Universal scaling dynamics at non-thermal fixed points in multi-component Bose gases far from equilibrium / Christian-Marcel Schmied ; Betreuer: Thomas Gasenzer." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1212729404/34.
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Salustiano, Helena Paula Rufino. "Caos e fractais na sala de aula." Master's thesis, Universidade de Évora, 2010. http://hdl.handle.net/10174/19963.
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O objectivo deste trabalho é o estudo do tema Caos e Fractais, com o propósito fundamental da sua implementação na sala de aula ou outro ambiente do Ensino Secundário. Com esse fim, é feita uma abordagem teórica dos conteúdos e são apresentadas algumas actividades a desenvolver com os alunos daquele nível de ensino. A introdução dos conceitos é feita de modo a possibilitar a sua leitura por um público mais geral, onde se incluem os alunos mais interessados e curiosos no tema. O estudo é acompanhado, sempre que possível, de exemplos e ilustrações gráficas. Para tal, foi utilizado o software Maxima (software livre) e outras aplicações interactivas disponíveis na Internet. ABSTRACT: The aim of this work is to study the theme of Chaos and Fractals, with the fundamental purpose of its implementation in the classroom, or in other environments of secondary school education. To carry out this aim a theoretical outlook of the contents will be provided alongside some activities to be undergone with students of that school level. The introduction to these concepts is open to the understanding of a larger audience, where we can include the most interested and curious students in this issue. The study is accompanied, whenever possible, with examples and graphics. To do so, the Maxima software (free software) was used, besides other interactive applications available on the Internet.
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Galves, Ana Paula Tremura. "O teorema de Lefschetz-Hopf e sua relação com outros teoremas clássicos da topologia /." São José do Rio Preto : [s.n.], 2009. http://hdl.handle.net/11449/94208.
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Orientador: Maria Gorete Carreira AndradeBanca: Denise de Mattos
Banca: Ermínia de Lourdes Campello Fanti
Resumo: Em Topologia, mais especificamente em Topologia Algébrica, temos alguns resultados clássicos que de alguma forma estão relacionados. No desenvolvimento deste trabalho, estudamos alguns desses resultados, a saber: Teorema de Lefschetz-Hopf, Teorema do Ponto Fixo de Lefschetz, Teorema do Ponto Fixo de Brouwer, Teorema da Curva de Jordan e o Teorema Clássico de Borsuk-Ulam. Além disso, tivemos como objetivo principal mostrar relações existentes entre esses teoremas a partir do Teorema de Lefschetz-Hopf.
Abstract: In Topology, more specifically in Algebraic Topology, we have some classical results that are in some way related. In developing this work, we studied some of these results, namely the Lefschetz-Hopf Theorem, the Lefschetz Fixed Point Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem and the Classic Borsuk-Ulam Theorem. Moreover, our main objective was to show relationships among those theorems by using Lefschetz-Hopf Theorem.
Mestre
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Tang, Shun. "Le théorème de concentration et la formule des points fixes de Lefschetz en géométrie d’Arakelov." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112015/document.
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Dans les années quatre-vingts dix du siècle dernier, R. W. Thomason a démontréun théorème de concentration pour la K-théorie équivariante algébrique sur lesschémas munis d’une action d’un groupe algébrique G diagonalisable. Comme d’habitude,un tel théorème entraîne une formule des points fixes de type Lefschetz qui permetde calculer la caractéristique d’Euler-Poincaré équivariante d’un G-faisceau cohérent surun G-schéma propre en termes d’une caractéristique sur le sous-schéma des points fixes.Le but de cette thèse est de généraliser les résultats de R.W. Thomason dans le contextede la géométrie d’Arakelov. Dans ce travail, nous considérons les schémas arithmétiquesau sens de Gillet-Soulé et nous tout d’abord démontrons un analogue arithmétiquedu théorème de concentration pour les schémas arithmétiques munis d’une action duschéma en groupe diagonalisable associé à Z/nZ. La démonstration résulte du théorèmede concentration algébrique joint à des arguments analytiques. Dans le dernier chapitre,nous formulons et démontrons deux types de formules de Lefschetz arithmétiques. Cesdeux formules donnent une réponse positive à deux conjectures énoncées par K. Köhler,V. Maillot et D. RösslerIn the nineties of the last century, R. W. Thomason proved a concentrationtheorem for the algebraic equivariant K-theory on the schemes which are endowed withan action of a diagonalisable group scheme G. As usual, such a concentration theoreminduces a fixed point formula of Lefschetz type which can be used to calculate theequivariant Euler-Poincaré characteristic of a coherent G-sheaf on a proper G-schemein terms of a characteristic on the fixed point subscheme. It is the aim of this thesis togeneralize R. W. Thomason’s results to the context of Arakelov geometry. In this work,we consider the arithmetic schemes in the sense of Gillet-Soulé and we first prove anarithmetic analogue of the concentration theorem for the arithmetic schemes endowedwith an action of the diagonalisable group scheme associated to Z/nZ. The proof is acombination of the algebraic concentration theorem and some analytic arguments. Inthe last chapter, we formulate and prove two kinds of arithmetic Lefschetz formulae.These two formulae give a positive answer to two conjectures made by K. Köhler, V.Maillot and D. Rössler
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CURCINO, Alexandre. "Avifauna em áreas de mineração: diversidade e conservação em Niquelândia e Barro Alto GO." Universidade Federal de Goiás, 2011. http://repositorio.bc.ufg.br/tede/handle/tde/2636.
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Previous issue date: 2011-03-25In the fixed point methodology, the observer remains for a predetermined time, recording all birds registered by observation or hearing. Widely used in temperate regions, the methodology has been used in Brazil, where it has suffered adaptations through the years. Whereas the current studies show different sampling times of methodology (10, 15 and 20 min), the aim of this survey was to compare the birds richness estimated for the sampling times of 10 and 20 minutes, in cerrado, gallery forest and vereda, in the regions of Niquelândia and Barro Alto - Goias and verify the effectiveness of bird detections per hour of study for different sampling situations and travel times between fixed points. The survey in Niquelândia occurred in 2007 and 2008. Barro Alto, in the years 2008 and 2009. At each location were established 20 point counts, and sampled five points between 6h00min and 8h40min. The points were drawn for 10 min and 20 min sampling . The results suggest that the researcher who remains 10 min at each point obtain the same statistical results that the researcher who remains 20 min at each point. The species detection efficiency is related to the balance in the choice of sampling time and displacement in order to increase the chances of finding rare species, and at the same time, maximize the number of detections.
Na metodologia de pontos fixos, o observador permanece parado por um tempo pré-determinado, anotando todas as aves registradas por observação ou audição Amplamente utilizada em regiões de clima temperado, a metodologia tem sido utilizada no Brasil, onde sofreu adaptações ao longo dos anos. Considerando que os estudos atuais apresentam diferentes tempos de amostragem para a metodologia de pontos fixos (em geral 10, 15 e 20 min), nosso objetivo foi comparar a riqueza de aves estimada para os tempos de amostragem de 10 e 20 minutos de permanência em cada ponto, em seis fitofisionomias de Cerrado e estimar a eficiência de detecções de aves por hora de estudo, com base no tempo de deslocamento e no tempo de permanência nos pontos. Foram realizadas 12 campanhas nas regiões de Niquelândia GO e 12 campanhas em Barro Alto GO. Em Niquelândia, as coletas ocorreram em 2007 e 2008. Em Barro Alto, nos anos de 2008 e 2009. Em cada local foram estabelecidos 20 pontos de observação, sendo amostrados cinco pontos após sorteio prévio, entre 6h00min e 8h40min. Os pontos foram sorteados de modo a alternarem amostragens de 10 min e de 20 min. Os resultados sugerem que o pesquisador que opta por permanecer 10 min em cada ponto obterá, ao final da amostragem, um número estatisticamente equivalente de novas espécies que o obtido pelo pesquisador que opta por permanecer 20 min em cada ponto. A eficiência de detecções de espécies está relacionada ao equilíbrio na escolha do tempo de amostragem e deslocamento de modo a aumentar as chances de encontrar espécies raras e, ao mesmo tempo, maximizar o número de detecções como um todo.
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Sera, Toru. "Functional limit theorem for occupation time processes of intermittent maps." Kyoto University, 2020. http://hdl.handle.net/2433/259719.
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Mateo, Garcia Ignacio de [Verfasser], Andreas [Akademischer Betreuer] Griewank, Nicolas R. [Akademischer Betreuer] Gauger, and Willy J. F. [Akademischer Betreuer] Govaerts. "Iterative matrix-free computation of Hopf bifurcations as Neimark-Sacker points of fixed point iterations / Ignacio de Mateo Garcia. Gutachter: Andreas Griewank ; Nicolas R. Gauger ; Willy J. F. Govaerts." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://d-nb.info/1020871148/34.
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Galves, Ana Paula Tremura [UNESP]. "O teorema de Lefschetz-Hopf e sua relação com outros teoremas clássicos da topologia." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/94208.
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galves_apt_me_sjrp.pdf: 719114 bytes, checksum: 3cc285d329c0d629cf2c6ff65c13a201 (MD5)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Em Topologia, mais especificamente em Topologia Algébrica, temos alguns resultados clássicos que de alguma forma estão relacionados. No desenvolvimento deste trabalho, estudamos alguns desses resultados, a saber: Teorema de Lefschetz-Hopf, Teorema do Ponto Fixo de Lefschetz, Teorema do Ponto Fixo de Brouwer, Teorema da Curva de Jordan e o Teorema Clássico de Borsuk-Ulam. Além disso, tivemos como objetivo principal mostrar relações existentes entre esses teoremas a partir do Teorema de Lefschetz-Hopf.
In Topology, more specifically in Algebraic Topology, we have some classical results that are in some way related. In developing this work, we studied some of these results, namely the Lefschetz-Hopf Theorem, the Lefschetz Fixed Point Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem and the Classic Borsuk-Ulam Theorem. Moreover, our main objective was to show relationships among those theorems by using Lefschetz-Hopf Theorem.
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Bethke, Matthias. "Approximation von Fixpunkten streng pseudokontraktiver Operatoren." Pädagogogische Hochschule “Liselotte Herrmann” Güstrow, 1989. https://slub.qucosa.de/id/qucosa%3A73375.
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In vorliegendem Artikel wird eine Verallgemeinerung eines Approximationsteorems von Chidume /6/ für streng pseudokontraktive Operatoren in Lp beziehungsweise lp-Räumen (mit P =2) angegeben. Es wird ein Verfahren betrachtet, welches von MANN /14/ für reelle Funktionen eingeführt würde.This article gives a generalization of an approximation theorem by Chidume / 6 / for strictly pseudocontractive operators in Lp or lp spaces (with P = 2). We consider a method, which MANN / 14 / had introduced for real functions.
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Boutaud, Pierre. "Branching random walk : limit cases and minimal hypothesis." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM025.
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La marche aléatoire branchante est un système de particules sur la droite réelle où partant au temps 0 d’une particule initiale en position 0, chaque particule vivante au temps n meurt au temps n + 1 en donnant indépendemment naissance à un nombre aléatoire de particules se dispersant aléatoirement autour de la position de la particule parente. Dans un premier chapitre introductif, nous définissons en détails le modèle de la marche aléatoire branchante ainsi que certains des enjeux de la recherche autour de ce modèle, notamment l’étude de la martingale additive. Cette martingale peut-être étudié au travers de sa convergence vers une limite triviale ou non ainsi que l’étude d’une renormalisation appropriée, dite de Seneta-Heyde, lorsque cette limite est triviale. Elle peut aussi être étudiée au travers d’équations récursives stochastiques menant à des équations de points fixes en loi. Cette dernière question correspond à des travaux non-publiés effectués en première année de thèse en continuité avec ceux effectués en mémoire de master. Le second chapitre est une traduction en anglais de certaines sections du précédent chapitre pour faciliter la compréhension de certains lecteurs sur les points importants de cette thèse.Dans un troisième chapitre nous présentons une nouvelle méthode de preuve développée avec Pascal Maillard pour le théorème d’Aïdékon et Shi sur la renormalisation de Seneta-Heyde de la martingale additive critique dans le cas où la marche de l’épine admet une variance finie. Cette nouvelle preuve se passe du recours à un lemme d’épluchage et à des calculs de seconds moments pour lui préférer une étude de la transformée de Laplace conditionnée. Les propriétés des fonctions de renouvellements permettent une approche plus générale qui ne demande pas de s’attarder en particulier sur la martingale dérivée. Ceci est d’ailleurs illustré dans le quatrième chapitre où dans de nou veaux travaux avec Pascal Maillard, nous trouvons la renormalisation de Seneta-Heyde de la martingale additive critique dans le cas où la marche de l’épine est dans le domaine d’attraction d’une loi stable. On voit alors que les fonctions de renouvellement nous fournissent un candidat mieux adapté à cette étude que la martingale dérivée, qui n’est plus toujours une martingale dans ce nouveau contexte.Enfin, le cinquième chapitre étudie la question de l’optimalité des hypothèses faites dans le chapitre précédent quant à la trivialité ou non de la limite obtenue après renormalisation de Seneta-HeydeThe branching random walk is a particle system on the real line starting at time 0 with an initial particle at position 0, then each particle living at time n proceeds to die at time n+1 and give birth, independently from the other particles of generation n, to a random number of particles at random positions. In a first chapter, we define in details the branching random walk model and some key elements of the scientific research on this model, including the study of the additive martingale. This martingale can be stuided through its convergence towards a limit that may be trivial, raising the question of an appropriate scaling, called Seneta-Heyde sclaing, in the case the limit is trivial. The additive martingale can also be studied with stochastic recursive equations lezading to fixed points equations in law. This latter question is adressed in some unpublished works from the first year of PhD, in continuioty with works from the masters thesis. The second chapter is a translation in english of some sections of the preivous chapter so that every reader can grasp the key elements and goals of this manuscript.In a third chapter, we present a new proof developed with Pascal Maillard for Aîdékon and Shi's theorem on the Seneta-Heyde scaling of the critical additive martingale in the finite variance case. This new proof no longer need a peeling lemma and the use of second moment arguments and prefers studying the conditional Laplace transform. the properties of some renewal functions allow a much more general approach without the need to foucs to much on the derivative martingale. This is also illustrated in a fourth chapter where in new works with Pascal Maillard, we find the Seneta-Heyde scaling for the critical additive martingale in the case where the spinal random walk is in the attraction domain of a stable law. We then observe that the renewal functions provide us with a better suited candidate for this study than the derivative artingale, which is no longer always a martingale in this context.Finally, the fifth chapter focus on the question of the optimality of the assumptions made in the preivous chapter concerning the non-triviality of the limit obtained with the Seneta-Heyde scaling
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Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.
Full textAbstract:
In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.
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Joshi, Nishant. "Universality and Individuality in Recurrent Networks extended to Biologically inspired networks." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-294208.
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Activities in the motor cortex are found to be dynamical in nature. Modeling these activities and comparing them with neural recordings helps in understanding the underlying mechanism for the generation of these activities. For this purpose, Recurrent Neural networks or RNNs, have emerged as an appropriate tool. A clear understanding of how the design choices associated with these networks affect the learned dynamics and internal representation still remains elusive. A previous work exploring the dynamical properties of discrete time RNN architectures (LSTM, UGRNN, GRU, and Vanilla) such as the fixed point topology and the linearised dynamics remains invariant when trained on 3 bit Flip- Flop task. In contrast, they show that these networks have unique representational geometry. The goal for this work is to understand if these observations also hold for networks that are more biologically realistic in terms of neural activity. Therefore, we chose to analyze rate networks that have continuous dynamics and biologically realistic connectivity constraints and on spiking neural networks, where the neurons communicate via discrete spikes as observed in the brain. We reproduce the aforementioned study for discrete architectures and then show that the fixed point topology and linearized dynamics remain invariant for the rate networks but the methods are insufficient for finding the fixed points of spiking networks. The representational geometry for the rate networks and spiking networks are found to be different from the discrete architectures but very similar to each other. Although, a small subset of discrete architectures (LSTM) are observed to be close in representation to the rate networks. We show that although these different network architectures with varying degrees of biological realism have individual internal representations, the underlying dynamics while performing the task are universal. We also observe that some discrete networks have close representational similarities with rate networks along with the dynamics. Hence, these discrete networks can be good candidates for reproducing and examining the dynamics of rate networks.Aktiviteter i motorisk cortex visar sig vara dynamiska till sin natur. Att modellera dessa aktiviteter och jämföra dem med neurala inspelningar hjälper till att förstå den underliggande mekanismen för generering av dessa aktiviteter. För detta ändamål har återkommande neurala nätverk eller RNN uppstått som ett lämpligt verktyg. En tydlig förståelse för hur designvalen associerade med dessa nätverk påverkar den inlärda dynamiken och den interna representationen är fortfarande svårfångad. Ett tidigare arbete som utforskar de dynamiska egenskaperna hos diskreta RNN- arkitekturer (LSTM, UGRNN, GRU och Vanilla), såsom fastpunkts topologi och linjäriserad dynamik, förblir oförändrad när de tränas på 3-bitars Flip- Flop-uppgift. Däremot visar de att dessa nätverk har unik representationsgeometri. Målet för detta arbete är att förstå om dessa observationer också gäller för nätverk som är mer biologiskt realistiska när det gäller neural aktivitet. Därför valde vi att analysera hastighetsnätverk som har kontinuerlig dynamik och biologiskt realistiska anslutningsbegränsningar och på spikande neurala nätverk, där neuronerna kommunicerar via diskreta spikar som observerats i hjärnan. Vi reproducerar den ovannämnda studien för diskreta arkitekturer och visar sedan att fastpunkts topologi och linjäriserad dynamik förblir oförändrad för hastighetsnätverken men metoderna är otillräckliga för att hitta de fasta punkterna för spiknätverk. Representationsgeometrin för hastighetsnätverk och spiknätverk har visat sig skilja sig från de diskreta arkitekturerna men liknar varandra. Även om en liten delmängd av diskreta arkitekturer (LSTM) observeras vara nära i förhållande till hastighetsnäten. Vi visar att även om dessa olika nätverksarkitekturer med varierande grad av biologisk realism har individuella interna representationer, är den underliggande dynamiken under uppgiften universell. Vi observerar också att vissa diskreta nätverk har nära representationslikheter med hastighetsnätverk tillsammans med dynamiken. Följaktligen kan dessa diskreta nätverk vara bra kandidater för att reproducera och undersöka dynamiken i hastighetsnät.
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Aguirre, John David Gómez. "Consequences of a dynamical gluon mass." reponame:Repositório Institucional da UFABC, 2017.
Find full textAbstract:
Orientador: Prof. Dr. Alysson Fábio FerrariTese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.
Na literatura encontramos argumentos tanto fenomenológicos quanto teóricos que favorecem o congelamento da constante de acoplamento da QCD a valores moderados no regime infravermelho. O acoplamento pode ser parametrizado em termos de uma massa efetiva para o gluon (mg) obtida dinamicamente através das equações de Schwinger- Dyson, cuja soluções são compatíveis com as simulações da QCD na rede. Primeiro nós consideramos o processo de aniquilação elétron-pósitron em hádrons Re+e- até O(3s) e adotamos o método de smearing sugerido por Poggio, Quinn e Weinberg para confrontar os dados experimentais com a teoria. Nós vamos usar como modelo teórico a QCD com uma constante de acoplamento finita no regime de baixas energias. Para encontrar o melhor fit entre os dados experimentais e teóricos, nós realizamos um test de 2, que dentro das incertezas do modelo , tem um valor mínimo quando mg=QCD está entre 1.2 - 1.4. Esses valores concordam com outras determinações fenomenológicas da razão mg=QCD e levam a uma carga efetiva s(0) 0.7. Nós comentamos como essas cargas efetivas poderiam afetar a escala de massa da dualidade global, a qual indica a fronteira entre a física perturbativa e não perturbativa. Calculamos tanto o potencial efetivo aprimorado no caso da QED escalar e da QCD com um escalar sem cor, como também a evolução do acoplamento escalar do Higgs () no Modelo Padrão. Em ambos os casos consideramos pontos fixos. No caso da QCD com o escalar sem carga de cor tanto a barreira associada ao polo de Landau quanto o mínimo do potencial mudam. Por outro lado, encontramos que a existência dos pontos fixos não perturbativos no infravermelho movem a evolução do acoplamento escalar na direcção da estabilidade. Para certos valores da constante de acoplamento da QCD no infravermelho, o potencial do Modelo Padrão pode ficar estável até a escala de Planck.
Several phenomenological and theoretical arguments favor a freezing of the Quantum Chromodynamics (QCD) coupling constant in the infrared region at one moderate value. This coupling can be parameterized in terms of an effective dynamical gluon mass (mg) which is determined through Schwinger-Dyson equations, whose solutions are compatible with QCD lattice simulations. First we consider the electron-positron annihilation process into hadrons Re+e- up to O(3s) and we adopt the smearing method suggest by Poggio, Quinn and Weinberg to confront the experimental data with theory. As a theoretical model we use the aforementioned QCD coupling constant frozen in the low energy regime. In order to find the best fit between experimental data and theory we perform a 2 study, that, within the uncertainties of the approach, has a minimum value when mg=QCD is in the range 1.2 - 1.4. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge s(0) 0.7. We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and nonperturbative physics. We also compute the improved effective potential in the case of scalar QED and QCD with a colorless scalar and compute the Standard Model scalar boson Higgs coupling () evolution. In both cases we consider fixed points. In the case of QCD with a colorless scalar not only the barrier associated to the Landau pole is changed but the local minimum of the potential is also changed. On the other hand we find that the existence of such nonperturbative infrared fixed point moves the evolution towards stability. For the phenomenological preferred IR value of the QCD coupling constant the standard model Higgs potential may be stable up to the Planck scale.