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1
BERATTO, EMANUELE. "Infrared properties of three dimensional gauge theories via supersymmetric indices." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2023. https://hdl.handle.net/10281/402369.
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The thesis focuses on the study of various supersymmetric three-dimensional gauge theories, mainly with at least N = 3 supersymmetry.
We range between very different theories and discuss several different aspects with the aim of validate our assumptions. Therefore, the leitmotiv of this work resides not so much in the topics we cover, but rather in the method that we use to obtain such results. This, in fact, consists in analysing the gauge invariant operators of the theory forming the so-called chiral ring. By having access to the chiral ring structure of the theory and to the operators forming it, we gain insight to the properties that needed to confirm or debunk our hypothesis.
We will essentially use two different tools for counting and studying such chiral operators: the Hilbert series and the three-dimensional superconformal index.
Thanks to the Hilbert series, we propose a quiver description for the mirror theories of the circle reduction of four-dimensional twisted χ(a2N) theories of class S. These mirrors are, in fact, described by "almost" star-shaped quivers containing both unitary and orthosymplectic gauge groups, along with hypermultiplets in the fundamental representation.
On the other hand, by means of the superconformal index, we investigate the N = 2 preserving exactly marginal operators of the so called S-fold theories. In particular, we focus on two families of such theories, constructed by gauging the diagonal flavour symmetry of the T(U(N)) and T[2,12][2,12 ](SU(4)) theories. In addition, we also examine in detail the zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis theories, with at least N = 6 supersymmetry, and with both orthosymplectic and unitary gauge groups. A number of dualities among all these theories are discovered and studied using the aforementioned tools.The thesis focuses on the study of various supersymmetric three-dimensional gauge theories, mainly with at least N = 3 supersymmetry. We range between very different theories and discuss several different aspects with the aim of validate our assumptions. Therefore, the leitmotiv of this work resides not so much in the topics we cover, but rather in the method that we use to obtain such results. This, in fact, consists in analysing the gauge invariant operators of the theory forming the so-called chiral ring. By having access to the chiral ring structure of the theory and to the operators forming it, we gain insight to the properties that needed to confirm or debunk our hypothesis. We will essentially use two different tools for counting and studying such chiral operators: the Hilbert series and the three-dimensional superconformal index. Thanks to the Hilbert series, we propose a quiver description for the mirror theories of the circle reduction of four-dimensional twisted χ(a2N) theories of class S. These mirrors are, in fact, described by "almost" star-shaped quivers containing both unitary and orthosymplectic gauge groups, along with hypermultiplets in the fundamental representation. On the other hand, by means of the superconformal index, we investigate the N = 2 preserving exactly marginal operators of the so called S-fold theories. In particular, we focus on two families of such theories, constructed by gauging the diagonal flavour symmetry of the T(U(N)) and T[2,12][2,12 ](SU(4)) theories. In addition, we also examine in detail the zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis theories, with at least N = 6 supersymmetry, and with both orthosymplectic and unitary gauge groups. A number of dualities among all these theories are discovered and studied using the aforementioned tools.
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Harris, Terri Joan Mrs. "HILBERT SPACES AND FOURIER SERIES." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/244.
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I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.
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Zhou, Shengtian. "Orbifold Riemann-Roch and Hilbert series." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/49768/.
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A general Riemann-Roch formula for smooth Deligne-Mumford stacks was obtained by Toen [Toë99]. Using this formula, we obtain an explicit Riemann-Roch formula for quasismooth substacks of weighted projective space, following the ideas in [Nir]. The Riemann-Roch formula enables us to study polarized orbifolds in terms of the associated Hilbert series. Given a polarized projectively Gorenstein quasismooth pair (X, Od∈Z O(d)), we want to parse the Hilbert series P(t) = ∑d>=0 h0(X,OX (d))td according to the orbifold loci. For X with only isolated orbifold points, we give a parsing such that each orbifold point corresponds to a closed term, which only depends on the orbifold type of the point and has Goresntein symmetry property and integral coefficients. Similarly, for the case when X has dimension <= 1 orbifold loci, we can also parse the Hilbert series into closed terms corresponding to orbifold curves and dissident points as well as isolated orbifold points. Our parsing of Hilbert series reflects the global symmetry property of the Gorenstein ring Od>=0 H0(X,OX (d))td in terms of its local data.
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Borkovitz, Debra Kay. "Maximal Hilbert series of quadratic-relator algebras." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/13231.
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Selig, Michael N. "On the Hilbert series of polarised orbifolds." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/77578/.
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We are interested in calculating the Hilbert series of a polarised orbifold (X;D) (that is D is an ample divisor on an orbifold X). Indeed, its numerical data is encoded in its Hilbert series, so that calculating this sometimes gives us information about the ring, notably possible generators and relations, using the Hilbert syzygies theorem. Vaguely, we have PX(t) = Num/Denom where Num is given by the relations and syzygies of R and Denom is given by the generators. Thus in particular we hope that we can use the numerical data of the ring to deduce possible explicit constructions. A reasonable goal is therefore to calculate the Hilbert series of a polarised (X;D); we write it in closed form, where each term corresponds to an orbifold stratum, is Gorenstein symmetric and with integral numerator of "short support". The study of the Hilbert series where the singular locus has dimension at most 1 leads to questions about more general rational functions of the form __N___ II(1-tai) with N integral and symmetric. We prove various parsings in terms of the poles at the Uai ; each individual term is Gorenstein symmetric, with integral numerator of "short support" and geometrically corresponds to some orbifold locus. Chapters 1 and 2 are expository material: Chapter 1 is basic introductory material whilst in Chapter 2 we explain the Hilbert series parsing in the isolated singularity case, as solved in Buckley et al. [2013] and Zhou [2011] and go over worked examples for practice. Chapter 3 uses the structure of the parsing in the isolated case and the expected structure in the non-isolated case to discuss generalisations to arbitrary rational functions with symmetry and poles only at certain roots of unity. We prove some special cases. Chapter 4 discusses the Hilbert series parsing in the curve orbifold locus case in a more geometrical setting. Chapter 5 discusses further generalisations and issues. In particular we discuss how the strategies used in Chapter 3 could work in a more general section, and the non symmetric case.
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Niese, Elizabeth M. "Combinatorial Properties of the Hilbert Series of Macdonald Polynomials." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26702.
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The original Macdonald polynomials $P_\mu$ form a basis for the vector space of symmetric
functions which specializes to several of the common bases such as the monomial, Schur, and
elementary bases. There are a number of different types of Macdonald polynomials obtained
from the original $P_\mu$ through a combination of algebraic and plethystic transformations one
of which is the modified Macdonald polynomial $\widetilde{H}_\mu$. In this dissertation, we study a certain
specialization $\widetilde{F}_\mu(q,t)$ which is the coefficient of $x_1x_2 ... x_N$ in $\widetilde{H}_\mu$ and also the Hilbert series
of the Garsia-Haiman module $M_\mu$. Haglund found a combinatorial formula expressing $\widetilde{F}_\mu$ as
a sum of $n!$ objects weighted by two statistics. Using this formula we prove a $q,t$-analogue of
the hook-length formula for hook shapes. We establish several new combinatorial operations
on the fillings which generate $\widetilde{F}_\mu$. These operations are used to prove a series of recursions
and divisibility properties for $\widetilde{F}_\mu$.Ph. D.
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Torri, Giuseppe. "Counting gauge invariant operators in supersymmetric theories using Hilbert series." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9989.
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In this thesis, the problem of counting gauge invariant operators in certain supersymmetric theories is discussed. These objects have a very important role in supersymmetric gauge theories, since they can be used to describe the space of zero-energy solutions, called moduli space, of such theories. In order to approach the counting problem, a technique is used based on a function known in Algebraic Geometry as the Hilbert series. For the examined theories, this can be considered a a partition function counting gauge invariant operators in the field theory according to their charges under quantum global symmetries. In the first part of the thesis, particular focus will be given to the application of the Hilbert series to conformal Chern-Simons theories living on the world-volume of M2-branes probing different toric Calabi-Yau 4-fold singularities. It will be shown how the Hilbert series can be combined with the brane tiling formalism to characterise the mesonic moduli space of vacua of a given theory through its generators and the relations they satisfy. Then, toric duality for these theories will be presented, with special attention to the role played by Hilbert series in making such feature manifest between two or more theories. Finally, Chern-Simons theories living on M2-branes probing cones over smooth toric Fano 3-folds and their mesonic Hilbert series will be presented. In the second part, it will be shown how the Hilbert series can be applied to counting gauge invariant operators in supersymmetric generalisations of Quantum Chromodynamics, known as SQCD theories. The discussion will hinge on a specific class of theories, with N multiplets transforming in the fundamental and anti-fundamental and one in the adjoint representation of the gauge group. For each classical group, the Hilbert series of the moduli space will be used to determine the dimension on the spaces, their generators and to argue that they are all Calabi-Yau manifolds.
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Tiwari, Sharwan Kumar [Verfasser]. "Algorithms in Noncommutative Algebras: Gröbner Bases and Hilbert Series / Sharwan Kumar Tiwari." München : Verlag Dr. Hut, 2017. http://d-nb.info/1149579307/34.
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Barrera, Salazar Daniel. "Cohomologie surconvergente des variétés modulaires de Hilbert et fonctions L p-adiques." Thesis, Lille 1, 2013. http://www.theses.fr/2013LIL10014/document.
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Pour une représentation automorphe cuspidale de GL(2,F) avec F un corps de nombres totalement réel, tel que est de type (k, r) et satisfait une condition de pente non critique, l’on construit une distribution p-adique sur le groupe de Galois de l’extension abélienne maximale de F non ramifiée en dehors de p et 1. On démontre que la distribution obtenue est admissible et interpole les valeurs critiques de la fonction L complexe de la représentation automorphe. Cette construction est basée sur l’étude de la cohomologie de la variété modulaire de Hilbert à coefficients surconvergentsFor each cohomological cuspidal automorphic representation for GL(2,F) where F is a totally real number field, such that is of type (k, r) tand satisfies the condition of non critical slope we construct a p-adic distribution on the Galois group of the maximal abelian extension of F unramified outside p and 1. We prove that the distribution is admissible and interpolates the critical values of L-function of the automorphic representation. This construction is based on the study of the overconvergent cohomology of Hilbert modular varieties
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Huang, Yongxiang. "ARBITRARY ORDER HILBERT SPECTRAL ANALYSIS DEFINITION AND APPLICATION TO FULLY DEVELOPED TURBULENCE AND ENVIRONMENTAL TIME SERIES." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2009. http://tel.archives-ouvertes.fr/tel-00439605.
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La Décomposition Modale Empirique (Empirical Mode Decomposition - EMD) ou la Transformation de Hilbert-Huang (HHT) est une nouvelle méthode d'analyse temps-fréquence qui est particulièrement adaptée pour des séries temporelles nonlinéaires et non stationnaires. Cette méthode a été proposée par NE. HUANG. il y a plus de dix ans. Pendant les dix dernières années, plus de 1000 articles ont appliqué cette méthode dans le cadre de diverses applications ou domaines de recherche. Dans cette thèse, nous appliquons cette méthode à des séries temporelles de turbulence, pour la première fois, et à des séries temporelles environnementales. Nous avons obtenu comme résultat le fait que la méthode EMD correspond à un banc de filtre dyadique (ou quasi-dyadique) pour la turbulence pleinement développée. Pour caractériser les propriétés intermittentes d'une série temporelle invariante d'échelle, nous avons généralisé l'analyse spectrale de Hilbert-Huang classique à des moments d'ordre arbitraire $q$, pour effectuer ce que nous avons appelé ``analyse spectrale de Hilbert d'ordre arbitraire''. Ceci fournit un nouveau cadre pour analyser l'invariance d'échelle directement dans un espace amplitude-fréquence, en estimant une intégrale marginale d'une pdf jointe $p(\omega,\mathcal{A})$ de la fréquence instantanée $\omega$ et de l'amplitude $\mathcal{A}$. Nous validons tout d'abord la méthode en analysant des séries temporelles de mouvement Brownien fractionnaire, et en analysant des séries temporelles multifractales synthétiques, en tant que modèle respectivement de processus monofractals et multifractals. Nous comparons les résultats obtenus avec la nouvelle méthode, à l'analyse classique utilisant les fonctions de structure: nous trouvons numériquement que la méthodologie utilisant l'approche de Hilbert fournit un estimateur plus précis pour le paramètre d'intermittence. Avec une hypothèse de stationarité, nous proposons un modèle analytique pour la fonction d'autocorrélation des incréments de séries temporelles de vitesse $\Delta u_{\ell}(t)$, où $\Delta u_{\ell}(t)=u(t+\ell)-u(t)$, et $\ell$ est l'incrément temporel. Dans le cadre de ce modèle, nous prouvons analytiquement que, si une loi de puissance est valide pour la série d'origine, la position minimisant la fonction d'autocorrélation de la variable d'origine est égale exactement au temps de séparation $\ell$ lorsque $\ell$ appartient à la zone invariante d'échelle. Ce modèle prédit une loi de puissance pour la valeur minimum, comportement vérifié par une simulation de mouvement Brownien fractionnaire et à partir de données expérimentales de turbulence. En introduisant une fonction cumulative pour la fonction d'autocorrélation, la contribution en échelle est alors caractérisée dans l'espace de fréquence de Fourier. Nous observons que la contribution principale à la fonction d'autocorrélation provient des grandes échelles. La même idée est appliquée à la fonction de structure d'ordre 2. Nous obtenons que celle-ci est également fortement influencée par les grandes échelles, ce qui montre que ceci n'est pas une bonne approche pour extraire les exposants invariants d'échelle d'une série temporelle lorsque les données sont caractérisées par des grandes échelles énergétiques. Nous appliquons ensuite cette méthodologie Hilbert-Huang à une base de données de turbulence homogène et presque isotrope, pour caractériser les propriétés multifractales invariantes d'échelle des série temporelles de vitesse en turbulence pleinement développée. Nous obtenons un comportement invariant d'échelle pour la pdf jointe $p(\omega,\mathcal{A})$ avec un exposant proche de la valeur de Kolmogorov. Nous estimons les exposants $\zeta(q)$ dans un espace amplitude-fréquence, pour la première fois. L'hypothèse d'isotropie est testée échelle par échelle dans l'espace amplitude-fréquence. Nous obtenons que le rapport d'isotropie généralisé décroit linéairement avec le moment $q$. Nous effectuons également l'analyse d'une série temporelle de température (scalaire passif) possédant un effet de rampe marqué (ramp-cliff). Pour ces données, l'approche traditionnelle utilisant les fonctions de structure ne fonctionne pas. Mais la nouvelle méthode développée dans cette thèse fournit un net régime invariant d'échelle jusqu'au moment $q=8$. Les exposants $\xi_{\theta}(q)-1$ sont très proches des exposants $\zeta(q)$ obtenus par l'approche des fonctions de structure pour la vitesse longitudinale. Nous nous intéressons ensuite à l'auto-similarité étendue (Extended Self Similarity - ESS) dans le cadre Hilbert-Huang. En ce qui concerne la méthode ESS, qui est devenue classique en turbulence, nous adaptons l'approche pour le cas Hilbert-Huang dans un espace de fréquence, et nous constatons que le modèle lognormal, avec un coefficient adéquat, fournit une très bonne estimation des exposants invariants d'échelle. Finalement nous appliquons la nouvelle méthodologie à des données environnementales: des débits de rivières, et des données de turbulence marine dans la zone de surf. Dans ce dernier cas, la méthode ESS permet de séparer les ondes de vent de la turbulence à petite échelle.
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Barns-Graham, Alexander Edward. "Much ado about nothing : the superconformal index and Hilbert series of three dimensional N =4 vacua." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/287950.
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We study a quantum mechanical $\sigma$-model whose target space is a hyperKähler cone. As shown by Singleton, [184], such a theory has superconformal invariance under the algebra $\mathfrak{osp}(4^*|4)$. One can formally define a superconformal index that counts the short representations of the algebra. When the hyperKähler cone has a projective symplectic resolution, we define a regularised superconformal index. The index is defined as the equivariant Hirzebruch index of the Dolbeault cohomology of the resolution, hereafter referred to as the index. In many cases, the index can be explicitly calculated via localisation theorems. By limiting to zero the fugacities in the index corresponding to an isometry, one forms the index of the submanifold of the target space invariant under that isometry. There is a limit of the fugacities that gives the Hilbert series of the target space, and often there is another limit of the parameters that produces the Poincaré polynomial for $\mathbb C^\times$-equivariant Borel-Moore homology of the space. A natural class of hyperKähler cones are Nakajima quiver varieties. We compute the index of the $A$-type quiver varieties by making use of the fact that they are submanifolds of instanton moduli space invariant under an isometry. Every Nakajima quiver variety arises as the Higgs branch of a three dimensional $\mathcal N =4$ quiver gauge theory, or equivalently the Coulomb branch of the mirror dual theory. We show the equivalence between the descriptions of the Hilbert series of a line bundle on the ADHM quiver variety via localisation, and via Hanany's monopole formula. Finally, we study the action of the Poisson algebra of the coordinate ring on the Hilbert series of line bundles. We restrict to the case of looking at the Coulomb branch of balanced $ADE$-type quivers in a certain infinite rank limit. In this limit, the Poisson algebra is a semiclassical limit of the Yangian of $ADE$-type. The space of global sections of the line bundle is a graded representation of the Poisson algebra. We find that, as a representation, it is a tensor product of the space of holomorphic functions with a finite dimensional representation. This finite dimensional representation is a tensor product of two irreducible representations of the Yangian, defined by the choice of line bundle. We find a striking duality between the characters of these finite dimensional representations and the generating function for Poincaré polynomials.
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Kidzinski, Lukasz. "Inference for stationary functional time series: dimension reduction and regression." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209226.
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Les progrès continus dans les techniques du stockage et de la collection des données permettent d'observer et d'enregistrer des processus d’une façon presque continue. Des exemples incluent des données climatiques, des valeurs de transactions financières, des modèles des niveaux de pollution, etc. Pour analyser ces processus, nous avons besoin des outils statistiques appropriés. Une technique très connue est l'analyse de données fonctionnelles (ADF).L'objectif principal de ce projet de doctorat est d'analyser la dépendance temporelle de l’ADF. Cette dépendance se produit, par exemple, si les données sont constituées à partir d'un processus en temps continu qui a été découpé en segments, les jours par exemple. Nous sommes alors dans le cadre des séries temporelles fonctionnelles.
La première partie de la thèse concerne la régression linéaire fonctionnelle, une extension de la régression multivariée. Nous avons découvert une méthode, basé sur les données, pour choisir la dimension de l’estimateur. Contrairement aux résultats existants, cette méthode n’exige pas d'assomptions invérifiables.
Dans la deuxième partie, on analyse les modèles linéaires fonctionnels dynamiques (MLFD), afin d'étendre les modèles linéaires, déjà reconnu, dans un cadre de la dépendance temporelle. Nous obtenons des estimateurs et des tests statistiques par des méthodes d’analyse harmonique. Nous nous inspirons par des idées de Brillinger qui a étudié ces models dans un contexte d’espaces vectoriels.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Schneider, Matti. "The Leray-Serre spectral sequence in Morse homology on Hilbert manifolds and in Floer homology on cotangent bundles." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-104619.
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The Leray-Serre spectral sequence is a fundamental tool for studying singular homology of a fibration E->B with typical fiber F. It expresses H (E) in terms of H (B) and H (F). One of the classic examples of a fibration is given by the free loop space fibration, where the typical fiber is given by the based loop space .
The first part of this thesis constructs the Leray-Serre spectral sequence in Morse homology on Hilbert manifolds under certain natural conditions, valid for instance for the free loop space fibration if the base is a closed manifold. We extend the approach of Hutchings which is restricted to closed manifolds. The spectral sequence might provide answers to questions involving closed geodesics, in particular to spectral invariants for the geodesic energy functional. Furthermore we discuss another example, the free loop space of a compact G-principal bundle, where G is a connected compact Lie group. Here we encounter an additional difficulty, namely the base manifold of the fiber bundle is infinite-dimensional. Furthermore, as H ( P) = HF (T P) and H ( Q) =HF (T Q), where HF denotes Floer homology for periodic orbits, the spectral sequence for P -> Q might provide a stepping stone towards a similar spectral sequence defined in purely Floer-theoretic terms, possibly even for more general symplectic quotients.
Hutchings’ approach to the Leray-Serre spectral sequence in Morse homology couples a fiberwise negative gradient flow with a lifted negative gradient flow on the base. We study the Morse homology of a vector field that is not of gradient type. The central issue in the Hilbert manifold setting to be resolved is compactness of the involved moduli spaces. We overcome this difficulty by utilizing the special structure of the vector field. Compactness up to breaking of the corresponding moduli spaces is proved with the help of Gronwall-type estimates. Furthermore we point out and close gaps in the standard literature, see Section 1.4 for an overview.
In the second part of this thesis we introduce a Lagrangian Floer homology on cotangent bundles with varying Lagrangian boundary condition. The corresponding complex allows us to obtain the Leray-Serre spectral sequence in Floer homology on the cotangent bundle of a closed manifold Q for Hamiltonians quadratic in the fiber directions. This corresponds to the free loop space fibration of a closed manifold of the first part. We expect applications to spectral invariants for the Hamiltonian action functional.
The main idea is to study pairs of Morse trajectories on Q and Floer strips on T Q which are non-trivially coupled by moving Lagrangian boundary conditions. Again, compactness of the moduli spaces involved forms the central issue. A modification of the compactness proof of Abbondandolo-Schwarz along the lines of the Morse theory argument from the first part of the thesis can be utilized.
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Hargis, Brent H. "Analysis of Long-Term Utah Temperature Trends Using Hilbert-Haung Transforms." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5490.
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We analyzed long-term temperature trends in Utah using a relatively new signal processing method called Empirical Mode Decomposition (EMD). We evaluated the available weather records in Utah and selected 52 stations, which had records longer than 60 years, for analysis. We analyzed daily temperature data, both minimum and maximums, using the EMD method that decomposes non-stationary data (data with a trend) into periodic components and the underlying trend. Most decomposition algorithms require stationary data (no trend) with constant periods and temperature data do not meet these constraints. In addition to identifying the long-term trend, we also identified other periodic processes in the data. While the immediate goal of this research is to characterize long-term temperature trends and identify periodic processes and anomalies, these techniques can be applied to any time series data to characterize trends and identify anomalies. For example, this approach could be used to evaluate flow data in a river to separate the effects of dams or other regulatory structures from natural flow or to look at other water quality data over time to characterize the underlying trends and identify anomalies, and also identify periodic fluctuations in the data. If these periodic fluctuations can be associated with physical processes, the causes or drivers might be discovered helping to better understand the system. We used EMD to separate and analyze long-term temperature trends. This provides awareness and support to better evaluate the extremities of climate change. Using these methods we will be able to define many new aspects of nonlinear and nonstationary data. This research was successful and identified several areas in which it could be extended including data reconstruction for time periods missing data. This analysis tool can be applied to various other time series records.
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Oneto, Alessandro. "Waring-type problems for polynomials : Algebra meets Geometry." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-129019.
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In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. At the same time, they are related to branches of Commutative Algebra and Algebraic Geometry. The classical Waring problem investigates decompositions of homogeneous polynomials as sums of powers of linear forms. Via Apolarity Theory, the study of these decompositions for a given polynomial F is related to the study of configuration of points apolar to F, namely, configurations of points whose defining ideal is contained in the ``perp'' ideal associated to F. In particular, we analyze which kind of minimal set of points can be apolar to some given polynomial in cases with small degrees and small number of variables. This let us introduce the concept of Waring loci of homogeneous polynomials. From a geometric point of view, questions about additive decompositions of polynomials can be described in terms of secant varieties of projective varieties. In particular, we are interested in the dimensions of such varieties. By using an old result due to Terracini, we can compute these dimensions by looking at the Hilbert series of homogeneous ideal. Hilbert series are very important algebraic invariants associated to homogeneous ideals. In the case of classical Waring problem, we have to look at power ideals, i.e., ideals generated by powers of linear forms. Via Apolarity Theory, their Hilbert series are related to Hilbert series of ideals of fat points, i.e., ideals of configurations of points with some multiplicity. In this thesis, we consider some special configuration of fat points. In general, Hilbert series of ideals of fat points is a very active field of research. We explain how it is related to the famous Fröberg's conjecture about Hilbert series of generic ideals. Moreover, we use Fröberg's conjecture to deduce the dimensions of several secant varieties of particular projective varieties and, then, to deduce results regarding some particular Waring-type problems for polynomials. In this thesis, we mostly work over the complex numbers. However, we also analyze the case of classical Waring decompositions for monomials over the real numbers. In particular, we classify for which monomials the minimal length of a decomposition in sum of powers of linear forms is independent from choosing the ground field as the field of complex or real numbers.
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REIS, Bruno Trindade. "Séries de Hilbert de algumas álgebras associadas a grafos orientados via cohomologia de conjuntos parcialmente ordenados." Universidade Federal de Goiás, 2011. http://repositorio.bc.ufg.br/tede/handle/tde/1948.
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Previous issue date: 2011-08-31We begin with a definition of the algebras Qn, who originated the study of algebra associated to directed graphs. Then, we define key concepts such as Hilbert series, graded and filtered algebras. Among the quadratic algebras, we introduce the Koszul algebras. The Hilbert series is a useful tool to study the Koszulity of a quadratic algebra. The homological interpretation of the coefficients of the Hilbert series of algebras associated with direct graphs allowed us to give conditions Koszulity these algebras in terms of the homological properties of the graph. We use this interpretation to construct algebras with Hilbert series prescribed.
Começamos definindo as álgebras Qn, que originaram o estudo das álgebras associadas a grafos orientados em níveis. Em seguida, definimos conceitos importantes, tais como séries de Hilbert , álgebras graduadas e álgebras filtradas. Entre as álgebras quadráticas, introduzimos as álgebras de Koszul. As séries de Hilbert são instrumentos úteis para estudar a Koszulidade de álgebras quadráticas. A interpretação homológica dos coeficientes da série de Hilbert de álgebras associadas a grafos em níveis nos permite dar condições de Koszulidade dessas álgebras em termos das propriedades homológicas do grafo. Usamos essa interpretação para construir álgebras com séries de Hilbert préestabelecidas.
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Georgiadis, Konstantinos. "Polarized Calabi-Yau threefolds in codimension 4." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16321.
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This work concerns the construction of Calabi-Yau threefolds in codimension 4. Based on a study of Hilbert series, we give a list of families of Calabi-Yau threefolds which may exist in codimension 3 and codimension 4. Using birational methods, we construct Calabi-Yau threefolds that realize several of the listed families. The main result is that the cases we consider in codimension 4 lie in two different deformation components.
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Schneider, Matti [Verfasser], Matthias [Akademischer Betreuer] Schwarz, and Alberto [Gutachter] Abbondandolo. "The Leray-Serre spectral sequence in Morse homology on Hilbert manifolds and in Floer homology on cotangent bundles / Matti Schneider ; Gutachter: Alberto Abbondandolo ; Betreuer: Matthias Schwarz." Leipzig : Universitätsbibliothek Leipzig, 2013. http://d-nb.info/123824257X/34.
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Klepsch, Johannes [Verfasser], Claudia [Akademischer Betreuer] [Gutachter] Klüppelberg, Alexander [Gutachter] Aue, and Klaus [Gutachter] Mainzer. "Time series analysis in Hilbert spaces : Estimation of functional linear processes and prediction of traffic / Johannes Klepsch ; Gutachter: Alexander Aue, Klaus Mainzer, Claudia Klüppelberg ; Betreuer: Claudia Klüppelberg." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1130323218/34.
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Barboza, Marcelo Bezerra. "Sobre uma classe de álgebras associadas a duas famílias de grafos orientados." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4541.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Given a directed layered graph , we present the algebra A() as a quotient of the free associative or tensor algebra (with unit, over an arbitrarily fixed field of scalars), freely generated by the set of edges in . We calculate the Hilbert series associated with the grading on A() coming from degree in the tensor algebra. We also calculate the group of automorphisms of A() that preserve the (ascending) filtration associated with the grading mentioned above. Despite the fact the main results within this notes remain true for a relatively large class of directed graphs, we stay close to the ones Dn and Ln, n 3, that is, those consisting, respectively, on the Hasse diagram of the partially ordered sets of faces in a regular polygon containing n edges and the power set of {1, . . . , n}. The work teaching us all of the above is [1], by Colleen Duffy.
Dado um grafo orientado em níveis, apresentamos a álgebra A() como um quociente da álgebra associativa livre ou tensorial (com unidade, sobre um corpo de escalares arbitrariamente fixado), livremente gerada pelo conjunto de arestas em . Calculamos a série de Hilbert associada à graduação em A() proveniente do grau na álgebra tensorial. Também calculamos o grupo dos automorfismos de A() que preservam a filtração (crescente) associada à graduação acima mencionada. Apesar de os resultados principais permanecerem verdadeiros para uma classe relativamente ampla de grafos orientados, permanecemos próximos a Dn e Ln, n 3, isto é, aqueles que consistem, respectivamente, no diagrama de Hasse dos conjuntos parcialmente ordenados das faces de um polígono regular de n lados e no conjunto das partes de {1, . . . , n}. O trabalho do qual aprendemos todo o acima é [1], por Collen Duffy.
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Dirino, Kariny de Andrade. "Um estudo sobre álgebras associadas a alguns grafos orientados em níveis." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7784.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Considering a layered directed graphs we may associate it to an algebra, denoted as , whose generators are the edges of the graph and the relations are defined through: every ways with the same initial vertex and the same final vertex determine different fractorizations for the same polynomial with coefficients in a non-commutative ring. We present a study about these algebras and their main properties, presenting some classes of examples and having as central focus the Hasse graph of the partially ordered set of k -faces of Petersen graph, . We discuss the results on basis for algebras of type we calculate their Hilbert series and the automorphisms group of these algebras, we determine the subgraphs induced by the set of vertices fixed by each and we calculate the graded trace generating functions, in order to introduce problems related to koszulity.
Dado um grafo orientado em níveis podemos associar a ele uma álgebra, denotada por cujos geradores são as arestas do grafo e as relações são definidas mediante: todos os caminhos com o mesmo vértice inicial e mesmo vértice final determinam fatorações distintas para o mesmo polinômio com coeficientes em um anel não comutativo. Exibimos um estudo sobre essas álgebras e suas principais propriedades, apresentando algumas classes de exemplos e tendo como foco central o grafo de Hasse do conjunto parcialmente ordenado das k-faces do grafo de Petersen, . Abordamos resultados sobre bases para álgebras do tipo , calculamos as suas séries de Hilbert e o grupo dos automorfismos dessas álgebras, determinamos os subgrafos induzidos pelo conjunto dos vértices fixados por cada e calculamos as funções geradoras do traço graduado, a fim de introduzirmos problemas relacionados à koszulidade.
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Góis, Aédson Nascimento. "Elementos da análise funcional para o estudo da equação da corda vibrante." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/6511.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESIn this work, we are treated some elements of functional analysis such as Banach spaces, inner product spaces and Hilbert spaces, also studied Fourier series and at the end briefly consider the equation of the vibrating string. With this, you realize that you do not need a lot of theory in order to get significant results.
Neste trabalho, são tratados alguns elementos da análise funcional como espaços de Banach, espaços com produto interno e espaços de Hilbert, estudamos também séries de Fourier e no final consideramos brevemente a equação da corda vibrante. Com isso, percebe-se que não se precisa de muita teoria para conseguirmos resultados significativos.
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Saide, Chafic. "Filtrage adaptatif à l’aide de méthodes à noyau : application au contrôle d’un palier magnétique actif." Thesis, Troyes, 2013. http://www.theses.fr/2013TROY0018/document.
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L’estimation fonctionnelle basée sur les espaces de Hilbert à noyau reproduisant demeure un sujet de recherche actif pour l’identification des systèmes non linéaires. L'ordre du modèle croit avec le nombre de couples entrée-sortie, ce qui rend cette méthode inadéquate pour une identification en ligne. Le critère de cohérence est une méthode de parcimonie pour contrôler l’ordre du modèle. Le modèle est donc défini à partir d'un dictionnaire de faible taille qui est formé par les fonctions noyau les plus pertinentes.Une fonction noyau introduite dans le dictionnaire y demeure même si la non-stationnarité du système rend sa contribution faible dans l'estimation de la sortie courante. Il apparaît alors opportun d'adapter les éléments du dictionnaire pour réduire l'erreur quadratique instantanée et/ou mieux contrôler l'ordre du modèle.La première partie traite le sujet des algorithmes adaptatifs utilisant le critère de cohérence. L'adaptation des éléments du dictionnaire en utilisant une méthode de gradient stochastique est abordée pour deux familles de fonctions noyau. Cette partie a un autre objectif qui est la dérivation des algorithmes adaptatifs utilisant le critère de cohérence pour identifier des modèles à sorties multiples.La deuxième partie introduit d'une manière abrégée le palier magnétique actif (PMA). La proposition de contrôler un PMA par un algorithme adaptatif à noyau est présentée pour remplacer une méthode utilisant les réseaux de neurones à couches multiplesFunction approximation methods based on reproducing kernel Hilbert spaces are of great importance in kernel-based regression. However, the order of the model is equal to the number of observations, which makes this method inappropriate for online identification. To overcome this drawback, many sparsification methods have been proposed to control the order of the model. The coherence criterion is one of these sparsification methods. It has been shown possible to select a subset of the most relevant passed input vectors to form a dictionary to identify the model.A kernel function, once introduced into the dictionary, remains unchanged even if the non-stationarity of the system makes it less influent in estimating the output of the model. This observation leads to the idea of adapting the elements of the dictionary to obtain an improved one with an objective to minimize the resulting instantaneous mean square error and/or to control the order of the model.The first part deals with adaptive algorithms using the coherence criterion. The adaptation of the elements of the dictionary using a stochastic gradient method is presented for two types of kernel functions. Another topic is covered in this part which is the implementation of adaptive algorithms using the coherence criterion to identify Multiple-Outputs models.The second part introduces briefly the active magnetic bearing (AMB). A proposed method to control an AMB by an adaptive algorithm using kernel methods is presented to replace an existing method using neural networks
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Afsharijoo, Pooneh. "Looking for a new version of Gordon's identities : from algebraic geometry to combinatorics through partitions." Thesis, Sorbonne Paris Cité, 2019. https://theses.md.univ-paris-diderot.fr/AFSHARIJOO_Pooneh_2_complete_20190510.pdf.
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Une partition d’un nombre entier positif n est une suite décroissante des entiers positifs dont la somme est égal à n. Les entiers qui y apparaissent sont appelés les parties de la partition. Ma thèse est centrée sur l’étude des partitions des nombres entiers et les identités qui les relient. Plus précisément, il s’agit de montrer que le nombre de partitions ayant une propriété A est égal au nombre de partitions ayant une autre propriété B. Ce type d’identité joue un rôle important en théorie des nombres, en combinatoire, en théorie de représentations et en physique statistique. Une de ces identités est la suivante: Théorème. (La première identité de Rogers-Ramanujan) Le nombre de partitions d’un nombre naturel n dont les parties sont congruentes à 1 ou 4 modulo 5 est égal au nombre de partitions de n dont les parties ne sont ni égales ni consécutives. Dans ce travail, on étudie les identités entre les partitions en utilisant la relation entre les combinatoires des partitions et les combinatoires de l’algèbre graduée associée à un objet important de la géométrie algèbrique: l’espace des arcs. Étant donnés un corps k de caractéristique zéro et des polynômes f1,…,fm de k[x1,…, xn], l’espace des arcs associé correspond à l’idéal I de S:=k[x1j,…, xnj|j>-1], engendré par les coefficients de certains développements associés aux polynômes ci-dessus et aux variables xij. Si on prend xi,0 = 0 pour i=1,…,n, la série de Hilbert-Poincaré de l’algèbre graduée S\I est étroitement liée aux partitions des entiers satisfaisants des conditions qui dépendent de l’idéal I. Dans le cas où f(x) = x^r de k[x], l’idéal I de k[x1, x2, … ] est un idéal différentiel pour la dérivation D(xi) = xi+1, dans le sens que DI est inclus dans I. En effet, dans ce cas I est engendré par x1^r et tous ses dérivés itérées. nous montrons que pour r = 2 le calcul de la base de Gröbner de l’ideal I par rapport à l’ordre lexicographique pondéré est lié à une identité faisant intervenir les partitions qui apparaissent dans la première identité de Rogers-Ramanujan. Nous prouvons ensuite qu’une base de Gröbner de cet idéal n’est pas différentiellement finie, au contraire du cas de l’ordre lexicographique inverse pondéré. Nous donnons une preuve de ce point de vue des identités de Gordon qui forment une famille importante d’identités reliant les partitions. En utilisant des idéaux différentiels et des méthodes venant de l’espace des arcs, nous énonçons une conjecture qui pourrait ajouter un nouveau membre aux identités de Gordon. Nous l’avons déjà démontré pour un cas particulier. À la fin, nous donnons une preuve simple et directe d’un théorème de Nguyen Duc Tam sur la base de Gröbner de l’idéal différentiel [x1y1]; Nous obtenons ensuite des identités entres les partitions avec 2 couleursA partition of a positive integer n is a decreasing sequence of positive integers such that their sum is equal to n. The integers which appear in this sequence are called the parts of this partition. My thesis studies the partitions of integers and the identities between them. A partition identity is an equality between the number of partitions of an integer n satisfying a certain condition A and the number of partitions of n satisfying another condition B. They play an important role in many areas: number theory, combinatorics, Lie theory, particle physics and statistical mechanics. One of these identities is as follows: Theorem. (The first Rogers-Ramanujan identity) The number of partitions of a positive integer n with no equal or consecutive parts is equal to the number of partitions of n into parts 1 or 4(mod.5). In this work, we study partition identities using the relation between the combinatorics of partitions and the combinatorics of graded algebras associated to an important object of algebraic geometry: arc spaces. Given a field k of characteristic zero and polynomials f1,…,fm in k[x1,…, xn], the associated arc space is the space corresponds to the ideal I of S:=k[x1j,…, xnj|j>-1], generated by the coefficients of some developments associated to the above polynomials and the variables xij. For focussed arcs, which is when we take xi0 = 0 for i=1,…,n, the Hilbert-Poincaré series of the graded algebra S\I is closely related to partitions of integers satisfying conditions depending on I. In the case where f(x) = x^r in k[x], the ideal I of k[x1, x2,… ] is a differential ideal for the derivation D(xi) = xi+1, in the sens that DI is included in I. In fact it is generated by x1^r and all its iterated derivatives. We show that when r = 2 the computation of a Gröbner basis of I with respect to the weighted lexicographical monomial order is related with an identity involving the partitions that appear in the first Rogers-Ramanujan identity. We then prove that a Gröbner basis of this ideal is not differentially finite in contrary with the case of the weighted reverse lexicographical order. We give a prove from this point of view of Gordon’s identities which is a family of important partitions identities. Using differential ideals we state a conjecture which could add a new member to Gordon’s identities. we prove then this conjecture for a special case. At the end, we give a simple and direct proof of a theorem of Nguyen Duc Tam about the Gröbner basis of the differential ideal [x1y1]; we then obtain identities involving partitions with 2 colors
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Marathe, Vikrant A. "Analog Single Sideband-Pulse Width Modulation Processor for Parametric Acoustic Arrays." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/2056.
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Parametric acoustic arrays are ultrasonic-based loudspeakers that produce highly directive audio. The audio must first be preprocessed and modulated into an ultrasonic carrier before being emitted into the air, where it will self-demodulate in the far field. The resulting audio wave is proportional to the double time-derivative of the square of the modulation envelope. This thesis presents a fully analog processor which encodes the audio into two Pulse Width Modulated (PWM) signals in quadrature phase and sums them together to produce a Single Sideband (SSB) spectrum around the fundamental frequency of the PWM signals. The two signals are modulated between 8% and 24% duty cycle to maintain a quasi-linear relationship between the duty cycle and the output signal level. This also allows the signals to sum without overlapping each other, maintaining a two-level output. The system drives a network of narrowband transducers with a center frequency equal to the PWM fundamental. Because the transducers are voltage driven, they have a bandpass frequency response which behaves as a first-order integrator on the SSB signal, eliminating the need for two integrators in the processor. Results show that the “SSB-PWM” output wave has a consistent 20-30dB difference in magnitude between the upper sideband and lower sideband. In simulation, a single tone test shows higher total harmonic distortion for lower frequencies and higher modulation depth. A two-tone test creates a 2nd order intermodulation term that increases with the frequencies of the input signals.
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Barkat, Braham. "Design, estimation and performance of time-frequency distributions." Thesis, Queensland University of Technology, 2000.
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Hussain, Zahir M. "Adaptive instantaneous frequency estimation: Techniques and algorithms." Thesis, Queensland University of Technology, 2002. https://eprints.qut.edu.au/36137/7/36137_Digitised%20Thesis.pdf.
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This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications.
Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis.
In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise.
Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise.
Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized.
For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis.
A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H.
An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent
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Scurek, Raymond Benjamin. "The projective representations of the extended Poincaré group and applications." Thesis, 2003. http://hdl.handle.net/2152/926.
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Scurek, Raymond Benjamin Böhm Arno. "The projective representations of the extended Poincaré group and applications." 2003. http://wwwlib.umi.com/cr/utexas/fullcit?p3122789.
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Uliczka, Jan. "Graded Rings and Hilbert Functions." Doctoral thesis, 2010. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201007066381.
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Die Arbeit basiert auf zwei Veröffentlichungen zur graduierten kommutativen Algebra: Thema des ersten Artikels ist die Übertragung eines klassischen Ergebnisses zur Höhe von Primidealen in Polynomringen auf allgemeine multigraduierte Ringe; einige Anwendungen für die multigraduierte Dimensionstheorie werden vorgestellt. Der zweite Artikel behandelt Hilbertreihen von Moduln über einem standard-graduierten Polynomring über einem Körper. Ausgehend von einem grundlegenden Ergebnis über gewisse formale Laurentreihen werden unter anderem die möglichen Hilbertreihen und h-Vektoren solcher Moduln charakterisiert.
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Hu, Chin-Ping, and 胡欽評. "Applications of the Hilbert-Huang Transform on the Non-stationary Astronomical Time Series." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/cs75nn.
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博士國立中央大學
天文研究所
103
The development of time-frequency analysis techniques made astronomers successfully deal with non-stationary time series that originated from unstable physical mechanisms. I applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), on two examples of non-stationary astrophysical phenomena: the superorbital modulation in a high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of a narrow-line Seyfert 1 active galactic nucleus (AGN) RE J1034+396. The high-mass X-ray binary SMC X-1 exhibits a superorbital modulation with a dramatically varying period ranging between ~40 days and ~60 days. A Hilbert spectrum that shows more detailed information in both the time and frequency domains was obtained using the light curve collected by the All-Sky Monitor onboard the Rossi X-ray Timing Explorer (RXTE). The RXTE observations show that the superorbital modulation period was mostly between ~50 days and ~65 days, whereas it changed to ~40 days around MJD 50,800 and MJD 54,000. Based on the instantaneous phase defined by the HHT, a superorbital profile, from which an asymmetric feature and a low state with barely any X-ray emissions (lasting for ~0.3 cycles) were observed. A positive correlation between the mean period and the amplitude of the superorbital modulation, which is similair to that in Her X-1, was also discovered. With the superorbital phase defined by the HHT, a phase-resolved analysis of both the spectra and the orbital profiles was processed. From all the spectral parameters, I noticed that the relation between the equivalent width of iron line and the plasma optical depth is not monotonic. There is no significant correlation for fluxes higher than ~35 mCrab but clear positive correlation when the intensity is lower than ~20 mCrab. This indicates that the iron line production is dominated by different regions of this binary system in different superorbital phases. Furthermore, a dip feature, similar to the pre-eclipse dip in Her X-1, lying at orbital phase ~0.6-0.85, was discovered during the superorbital transition state. This indicates that the accretion disk has a bulge that absorbs considerable X-ray emission in the stream-disk interaction region. The dip width is anti-correlated with the flux, and this relation can be interpreted by the precessing tilted accretion disk scenario. With the successful experience of dealing with the superorbital modulation of an X-ray binary system, we further applied the HHT to analyze the QPO of RE J1034+396 using the data collected by XMM-Newton in 2007. RE J1034+396, a narrow-line Seyfert 1 galaxy, is the first example of AGNs that exhibited a nearly coherent QPO. The ensemble empirical mode decomposition (EEMD) provides bandpass-filtered data that can be used in the O - C and correlation analysis. From the Hilbert spectrum and the O - C analysis, I suggested that it is better to divide the evolution of the QPO in this observation into three epochs according to their different periodicities. Besides the periodicities, the correlations between the QPO periods and corresponding mean count rates are also different in these three epochs. The change in periodicity and the relationships could be interpreted by the change in oscillation mode based on the assumption of diskoseismology model. Finally, we found no significant phase lags between the soft and hard X-ray bands, which is also confirmed in the QPO phase-resolved spectral analysis. Finally, I presented a brief summary and pointed out possible future applications of the HHT on other astronomical time series, as well as the possible application of two-dimensional EEMD on morphological analysis.
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Hong, Jian-Yi, and 洪健儀. "Financial Time Series Prediction Model Based on Hilbert-Huang Transform and Artificial Neural Network." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/a684vz.
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碩士國立臺北科技大學
商業自動化與管理研究所
98
The time series prediction method was usually limited by the non-linearity and non-stationary of the financial time series data. As a result, Hilbert-Huang transform (HHT) was adapted in this paper. Through the processes of the empirical mode decomposition (EMD), the time series data could be decomposed into intrinsic mode function (IMF) components. Therefore, important patterns in different frequency spaces could be shown. Further, Testing-and-Acceptance method was used to sort the IMF components according to their importance to filter out the noise. Finally, the IMF components which are not noises were used to be the input variables of the back-propagation neural network method. The empirical results show that Hilbert spectrum analysis could be effectively used to explain the important characteristic of the financial time series. Further, the empirical results also demostrate that the back-propagation neural network forecasting model can accurately predict with Hilbert-Huang transform.
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Söger, Christof. "Parallel Algorithms for Rational Cones and Affine Monoids." Doctoral thesis, 2014. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2014042212422.
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This thesis presents parallel algorithms for rational cones and affine monoids which pursue two main computational goals: finding the Hilbert basis, a minimal generating system of the monoid of lattice points of a cone; and counting elements degree-wise in a generating function, the Hilbert series.
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Weng, Hai-Hsing, and 翁海馨. "Application of Hilbert-Huang Transform Method in Late Quaternary Equatorial Pacific Climate Time-Series Analysis." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/94463712197811578498.
Full textAbstract:
碩士國立臺灣海洋大學
應用地球科學研究所
96
A new time series analysis method, HHT (Hilbert-Huang Transform), is applied in studying late Quaternary equatorial Pacific SST variations over orbital time scales. A LAPAS (Late Quaternary Equatorial Pacific Climate Time Series) SST data set which was compiled based on four marine SST records of the past 800,000 years: ODP846, ODP806B, MD972140 and MD972142 from the equatorial Pacific, was used in testing the HHT and also comparing the HHT results to those of the FFT (Fast Fourier Transform) that has been used extensively in paleoclimatic time series analyses. HHT is an adaptive time series analysis method more suitable than FFT for decomposing nonlinear and nonstationary time series. In testing the HHT and FFT by LAPAS SST data, this study found that similar spectra with consistent average estimates of coherency and phase were shown by both methods over three primary orbital frequencies (eccentricity, tilt, and precession). The IMFs (Intrinsic Mode Function) decomposed from EMD (Empirical Mode Decomposition) in applying the HHT in the LAPAS, however, show much stable estimates of instantaneous phases and amplitudes over time than those filtered by FFT, suggesting the HHT is a more suitable method for analyzing paleoclimatic data. This study shows that over the 100 kyr cycle, the maxima of equator Pacific SST leads the minima of global ice volume over the past 800,000 year. The phase relationship is consistent with what is observed from the atmospheric pCO2 record reconstructed from Antarctic ice cores, in which the pCO2 increases also precede the rapid melting of Northern Hemisphere ice sheet, implying that the equatorial Pacific SST is probably controlled by global green house effects or carbon cycling perturbations. Over the 41kyr and the 23kyr cycles, the maxima of equatorial Pacific SST lag slightly the maxima in incoming solar insolation that have been controlled by the tilt and precession variations, suggesting that the equatorial Pacific SST has been determined by latitudinal and seasonal redistributions of incoming solar insolation caused by the orbital forcing. This study suggests that over three primary orbital cycles, the changes in atmospheric green house concentrations, incoming solar insolation, and other possible feedback processes in Earth’s climate system, all play important role in determining the amplitude and timing of SST variations in the equatorial Pacific.
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Chien, Jing-jung, and 錢映蓉. "Classification and Hilbert Series of Irreducible Algebraic Curves of Degree Four with Three Double Points." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/20451791474744322273.
Full textAbstract:
碩士國立中正大學
數學所
98
We try to classify irreducible projective curves of degree three and irreducible projective curves of degree four with three double points. Then we observe that there exist representatives of these curves. Then we find some Hilbert-Samuel functions and Hilbert series by these representatives.
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Brinkmann, Daniel. "Hilbert-Kunz functions of surface rings of type ADE." Doctoral thesis, 2013. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2013082711496.
Full textAbstract:
We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal
Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals.
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Lu, Tsung-Che, and 呂宗哲. "Compact Circular Polarization Fractal Antenna with Series Hilbert Curve Configurations for WLAN 2.4/5 GHzDual-Band Applications." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/49890139234492712818.
Full textAbstract:
碩士逢甲大學
電機工程所
96
Uses a space filling technique with series Hilbert curve configuration for 2.4/5 GHz dual-band design and to represent the performance of wide-band, circular polarization and small size. Basically, it is a novel dual-band fractal antenna with the combination of Hilbert curve and monopole. In practice, the configuration of dual-band fractal antenna is proposed by the iteration technique of Hilbert curve and the surface distribution; meantime, the design parameters included substrate size, feed-line length/width, ground plane, Hilbert curve length/width and iterations are analyzed for the desired S11 frequency responses and the circular polarization radiation patterns. For applications, it can be applied for WLAN, wireless PDA and smart phone etc.
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Schneider, Matti. "The Leray-Serre spectral sequence in Morse homology on Hilbert manifolds and in Floer homology on cotangent bundles." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A11833.
Full textAbstract:
The Leray-Serre spectral sequence is a fundamental tool for studying singular homology of a fibration E->B with typical fiber F. It expresses H (E) in terms of H (B) and H (F). One of the classic examples of a fibration is given by the free loop space fibration, where the typical fiber is given by the based loop space .
The first part of this thesis constructs the Leray-Serre spectral sequence in Morse homology on Hilbert manifolds under certain natural conditions, valid for instance for the free loop space fibration if the base is a closed manifold. We extend the approach of Hutchings which is restricted to closed manifolds. The spectral sequence might provide answers to questions involving closed geodesics, in particular to spectral invariants for the geodesic energy functional. Furthermore we discuss another example, the free loop space of a compact G-principal bundle, where G is a connected compact Lie group. Here we encounter an additional difficulty, namely the base manifold of the fiber bundle is infinite-dimensional. Furthermore, as H ( P) = HF (T P) and H ( Q) =HF (T Q), where HF denotes Floer homology for periodic orbits, the spectral sequence for P -> Q might provide a stepping stone towards a similar spectral sequence defined in purely Floer-theoretic terms, possibly even for more general symplectic quotients.
Hutchings’ approach to the Leray-Serre spectral sequence in Morse homology couples a fiberwise negative gradient flow with a lifted negative gradient flow on the base. We study the Morse homology of a vector field that is not of gradient type. The central issue in the Hilbert manifold setting to be resolved is compactness of the involved moduli spaces. We overcome this difficulty by utilizing the special structure of the vector field. Compactness up to breaking of the corresponding moduli spaces is proved with the help of Gronwall-type estimates. Furthermore we point out and close gaps in the standard literature, see Section 1.4 for an overview.
In the second part of this thesis we introduce a Lagrangian Floer homology on cotangent bundles with varying Lagrangian boundary condition. The corresponding complex allows us to obtain the Leray-Serre spectral sequence in Floer homology on the cotangent bundle of a closed manifold Q for Hamiltonians quadratic in the fiber directions. This corresponds to the free loop space fibration of a closed manifold of the first part. We expect applications to spectral invariants for the Hamiltonian action functional.
The main idea is to study pairs of Morse trajectories on Q and Floer strips on T Q which are non-trivially coupled by moving Lagrangian boundary conditions. Again, compactness of the moduli spaces involved forms the central issue. A modification of the compactness proof of Abbondandolo-Schwarz along the lines of the Morse theory argument from the first part of the thesis can be utilized.
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Peng, Yonghong. "Empirical Model Decomposition based Time-Frequency Analysis for Tool Breakage Detection." 2006. http://hdl.handle.net/10454/3178.
Full textAbstract:
NoExtensive research has been performed to investigate effective techniques, including advanced sensors and new monitoring methods, to develop reliable condition monitoring systems for industrial applications. One promising approach to develop effective monitoring methods is the application of time-frequency analysis techniques to extract the crucial characteristics of the sensor signals. This paper investigates the effectiveness of a new time-frequency analysis method based on Empirical Model Decomposition and Hilbert transform for analyzing the nonstationary cutting force signal of the machining process. The advantage of EMD is its ability to adaptively decompose an arbitrary complicated time series into a set of components, called intrinsic mode functions (IMFs), which has particular physical meaning. By decomposing the time series into IMFs, it is flexible to perform the Hilbert transform to calculate the instantaneous frequencies and to generate effective time-frequency distributions called Hilbert spectra. Two effective approaches have been proposed in this paper for the effective detection of tool breakage. One approach is to identify the tool breakage in the Hilbert spectrum, and the other is to detect the tool breakage by means of the energies of the characteristic IMFs associated with characteristic frequencies of the milling process. The effectiveness of the proposed methods has been demonstrated by considerable experimental results. Experimental results show that (1) the relative significance of the energies associated with the characteristic frequencies of milling process in the Hilbert spectra indicates effectively the occurrence of tool breakage; (2) the IMFs are able to adaptively separate the characteristic frequencies. When tool breakage occurs the energies of the associated characteristic IMFs change in opposite directions, which is different from the effect of changes of the cutting conditions e.g. the depth of cut and spindle speed. Consequently, the proposed approach is not only able to effectively capture the significant information reflecting the tool condition, but also reduces the sensitivity to the effect of various uncertainties, and thus has good potential for industrial applications.
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(11186268), Razan Taha. "p-adic Measures for Reciprocals of L-functions of Totally Real Number Fields." Thesis, 2021.
Find full textAbstract:
We generalize the work of Gelbart, Miller, Pantchichkine, and Shahidi on constructing p-adic measures to the case of totally real fields K. This measure is the Mellin transform of the reciprocal of the p-adic L-function which interpolates the special values at negative integers of the Hecke L-function of K. To define this measure as a distribution, we study the non-constant terms in the Fourier expansion of a particular Eisenstein series of the Hilbert modular group of K. Proving the distribution is a measure requires studying the structure of the Iwasawa algebra.