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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
41

Generating Functions : Powerful Tools for Recurrence Relations. Hermite Polynomials Generating Function

Rydén, Christoffer January 2023 (has links)
In this report we will plunge down in the fascinating world of the generating functions. Generating functions showcase the "power of power series", giving more depth to the word "power" in power series. We start off small to get a good understanding of the generating function and what it does. Also, off course, explaining why it works and why we can do some of the things we do with them. We will see alot of examples throughout the text that helps the reader to grasp the mathematical object that is the generating function. We will look at several kinds of generating functions, the main focus when we establish our understanding of these will be the "ordinary power series" generating function ("ops") that we discuss before moving on to the "exponential generating function" ("egf"). During our discussion on ops we will see a "first time in literature" derivation of the generating function for a recurrence relation regarding "branched coverings". After finishing the discussion regarding egf we move on the Hermite polynomials and show how we derive their generating function. Which is a generating function that generates functions. Lastly we will have a quick look at the "moment generating function".
42

Relative Fontaine-Laffaille Theory over Power Series Rings

Christian Lawrence Hokaj (18368760) 16 April 2024 (has links)
<p dir="ltr">Let k be a perfect field of characteristic p > 2. We extend the equivalence of categories between Fontaine-Laffaille modules and Z_p lattices inside crystalline representations with Hodge-Tate weights at most p-2 of Fontaine to the situation where the base ring is the power series ring in d variables over the ring of Witt vectors of k. </p>
43

Inference in Power Series Distributions

Korte, Robert A. 16 November 2012 (has links)
No description available.
44

On the Structure of Kronecker Function Rings and Their Generalizations

McGregor, Daniel 02 August 2018 (has links)
No description available.
45

On Rational and Periodic Power Series and on Sequential and Polycyclic Error-Correcting Codes

Parra Avila, Benigno Rafael January 2009 (has links)
No description available.
46

Mikroprimstellen für p-adische Zahlkörper

Wirl, Ernst Ludwig 14 February 2011 (has links)
Mikroprimstellen wurden eingeführt von J. Neukirch im Rahmen der abstrakten Klassenkörpertheorie. Eine Verallgemeinerung der Zerlegungsgruppen von Primstellen globaler Körper motivierte die rein gruppentheoretische Definition der Mikroprimstellen als gewisse Äquivalenzklassen von Frobeniuselementen. Auf den Fall der Galoisgruppen lokaler oder globaler Körper angewendet, ergibt diese Theorie eine Beschreibung spezieller Konjugationsklassen. Die Hauptaufgabe von J. Neukirch ist, die zahlentheoretische Bedeutung der Mikroprimstellen zu verstehen, das heißt, sie in Termen des Grundkörpers anzugeben. J. Mehlig und E.-W. Zink fanden eine Bijektion zwischen Mikroprimstellen und normverträglichen Folgen von Primelementen in Körpertürmen. Diese Türme entstehen durch die Fixkörper der abgeleiteten Untergruppen der Trägheitsgruppe. Auf diese Weise betrachtet man Mikroprimstellen für die entsprechenden Faktorgruppen der absoluten Galoisgruppe, um dann einen projektive Limes zu bilden. Im ersten Schritt ist eine Bijektion zwischen relativen Mikroprimstellen und Konjugationsklassen von Primelementen gezeigt worden. Das Hauptergebnis dieser Arbeit ist eine vollständige Antwort auf die Frage von J. Neukirch im zweiten Schritt. Es wird eine Normabbildung für Lubin-Tate-Potenzreihen verschiedener Höhe angegeben und der projektive Limes bezüglich dieser Normabbildungen gebildet. Dazu werden Ergebnisse der Klassenkörpertheorie auf einen ''''fastabelschen'''' Fall übertragen. Schließlich können die Mikroprimstellen als Galoisorbits von normverträglichen Abfolgen normischer Lubin-Tate-Potenzreihen beschrieben werden. Die Koeffizienten aller dieser Lubin-Tate-Potenzreihen sind in einer endlichen unverzweigten Erweiterung des Grundkörpers. Also kann man zu einer gegebenen normverträglichen Abfolge normischer Lubin-Tate-Potenzreihen den Koeffizientenkörper definieren. Der Grad dieses Körpers bzw. die Länge des Galoisorbits entspricht dem Grad der zugehörigen Mikroprimstelle. / Micro primes were introduced by J. Neukirch in the context of abstract class field theory. A generalization of decomposition groups of primes of global fields led him to a purely group theoretical definition of micro primes as certain equivalence classes of Frobenius elements. Applied to the case of Galois groups of local or global fields this theory yields a description of special conjugacy classes. The main problem already posed by J. Neukirch is to understand the number theoretical meaning of micro primes, that is to describe them in terms of the base field. J. Mehlig and E.-W. Zink established a bijection between micro primes and norm compatible sequences of prime elements in field towers. These towers arise as fixed point fields for the sequence of derived subgroups of the inertia group. So one has to study micro primes for the corresponding factor groups of the absolute Galois group and then to form a projective limit. In the first step, a bijection between relative micro primes and conjugacy classes of prime elements has been obtained. The main result of this project is a complete answer to the problem of J. Neukirch for the second step. One has to introduce norm maps between Lubin-Tate power series of different height and the projective limit has to be taken with respect to these norm maps. For this purpose results from class field theory are transferred to an ''''almost abelian'''' case. In the end micro primes can be described as Galois orbits of norm compatible sequences of normic Lubin-Tate power series. The coefficients of all the Lubin-Tate power series are in finite unramified extensions of the base field. Therefore one can define a field of coefficients for a given norm compatible sequence of normic Lubin-Tate power series. The degree of that field respectively the length of the Galois orbit is at the same time the degree of the corresponding micro prime.
47

Distribuições k-modificadas da família série de potência uniparamétrica / k-Modified distributions of the uniparametric power series family

Carvalho, Sergio Ozorio de 23 May 2017 (has links)
Neste trabalho é proposta a família de distribuições Série de Potência k-Modificadas para modelar conjuntos de dados de contagem que apresentam ou não alguma discrepância na frequência da observação k em relação à distribuição Série de Potência associada. É importante ressaltar que o emprego do termo Modificada(s) não possui o mesmo contexto ao empregado por Gupta (1974), o qual introduziu a classe de distribuições Série de Potência Modificadas representada pela sigla MPSD. Neste trabalho, entende-se por modificação, a inclusão de um parâmetro na função massa de probabilidade da distribuição Série de Potência tornando essa nova família de distribuições capaz de modelar adequadamente conjunto de dados para os casos em que há excesso (inflação), falta (deflação), ausência ou até mesmo quando a frequência da observação k estiver de acordo para a suposição de uma distribuição pertencente à família Série de Potência. Para esta nova família de distribuições são apresentadas propriedades como Função de distribuição, Função característica, Função geradora de momentos, Estatísticas de Ordem dentre outras, além de contextualizá-la como modelo de mistura. As distribuições consideradas para a construção dessa nova família serão as distribuições uniparamétricas pertencentes à família Série de Potência, cuja função massa de probabilidade pode ser escrita em função de sua média. / In this work, it is proposed the family of k-modified power series distributions to model count data sets that may or may not present some discrepancy in the frequency of the observation k in relation to the power series distribution associated. It is important to highlight that employing the term \"modified\" does not imply the same context to the one employed by Gupta (1974), which introduced the class of power series modified distributions represented by the acronym MPSD. In this work, modification can be understood as the inclusion of a parameter in the probability mass function of the power series distribution, allowing this family of distributions to properly model a data set for cases where there is an excess (inflation), deficiency (deflation), lack or even when the frequency of observations k are in agreement with the supposition of a distribution belonging to the power series family. It is presented, for this new family of distributions, properties like distribution function, characteristic function, moment generating function, order statistics, among others. Moreover the family is also contextualized as a mixture model. The distributions considered to construct this new family are uniparametric and belong to the power series family, for which the probability mass can be written as function of its mean.
48

Distribuições k-modificadas da família série de potência uniparamétrica / k-Modified distributions of the uniparametric power series family

Sergio Ozorio de Carvalho 23 May 2017 (has links)
Neste trabalho é proposta a família de distribuições Série de Potência k-Modificadas para modelar conjuntos de dados de contagem que apresentam ou não alguma discrepância na frequência da observação k em relação à distribuição Série de Potência associada. É importante ressaltar que o emprego do termo Modificada(s) não possui o mesmo contexto ao empregado por Gupta (1974), o qual introduziu a classe de distribuições Série de Potência Modificadas representada pela sigla MPSD. Neste trabalho, entende-se por modificação, a inclusão de um parâmetro na função massa de probabilidade da distribuição Série de Potência tornando essa nova família de distribuições capaz de modelar adequadamente conjunto de dados para os casos em que há excesso (inflação), falta (deflação), ausência ou até mesmo quando a frequência da observação k estiver de acordo para a suposição de uma distribuição pertencente à família Série de Potência. Para esta nova família de distribuições são apresentadas propriedades como Função de distribuição, Função característica, Função geradora de momentos, Estatísticas de Ordem dentre outras, além de contextualizá-la como modelo de mistura. As distribuições consideradas para a construção dessa nova família serão as distribuições uniparamétricas pertencentes à família Série de Potência, cuja função massa de probabilidade pode ser escrita em função de sua média. / In this work, it is proposed the family of k-modified power series distributions to model count data sets that may or may not present some discrepancy in the frequency of the observation k in relation to the power series distribution associated. It is important to highlight that employing the term \"modified\" does not imply the same context to the one employed by Gupta (1974), which introduced the class of power series modified distributions represented by the acronym MPSD. In this work, modification can be understood as the inclusion of a parameter in the probability mass function of the power series distribution, allowing this family of distributions to properly model a data set for cases where there is an excess (inflation), deficiency (deflation), lack or even when the frequency of observations k are in agreement with the supposition of a distribution belonging to the power series family. It is presented, for this new family of distributions, properties like distribution function, characteristic function, moment generating function, order statistics, among others. Moreover the family is also contextualized as a mixture model. The distributions considered to construct this new family are uniparametric and belong to the power series family, for which the probability mass can be written as function of its mean.
49

Distribuições k-modificadas da família Série de Potência uniparamétrica / K-modified distributions of the family uni-parametric Power Series

Carvalho, Sérgio Ozório de 23 May 2017 (has links)
Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2017-10-10T18:05:40Z No. of bitstreams: 1 DissSOC.pdf: 1290080 bytes, checksum: 3b1d7f1f88c287f6fc22d678e2f968ed (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-25T12:27:04Z (GMT) No. of bitstreams: 1 DissSOC.pdf: 1290080 bytes, checksum: 3b1d7f1f88c287f6fc22d678e2f968ed (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-25T12:27:14Z (GMT) No. of bitstreams: 1 DissSOC.pdf: 1290080 bytes, checksum: 3b1d7f1f88c287f6fc22d678e2f968ed (MD5) / Made available in DSpace on 2018-01-25T12:31:09Z (GMT). No. of bitstreams: 1 DissSOC.pdf: 1290080 bytes, checksum: 3b1d7f1f88c287f6fc22d678e2f968ed (MD5) Previous issue date: 2017-05-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / This paper proposes a family of distributions Power Series k-Modified from to model sets of count data which have or not any discrepancy in the frequency of observation k in relation to the distribution associated Power Series. Is understood as a modification, inclusion of a parameter in the mass function of probability of the distribution Power Series, making this new family of distributions able to adequately model the data set in cases where there is excess (inflation), poor (deflation) the absence or even when the frequency of the observations k is according to the distribution power series. For this new family of distributions are presented some properties as the distribution functions, Statistics Order among others, besides contextualizes it as mixing model and place it in the context of regression models. The distributions considered for the construction of this new family will be uni-parametric distributions belonging to the Power Series family, whose probability mass function can be written in terms of their average. / Neste trabalho é proposta a família de distribuições Série de Potência k-Modificadas para modelar conjuntos de dados de contagem que apresentam ou não alguma discrepância na frequência da observação k em relação à distribuição Série de Potência associada. É importante ressaltar que o emprego do termo Modificada(s) não possui o mesmo contexto ao empregado por Gupta (1974), o qual introduziu a classe de distribuições Série de Potência Modificadas representada pela sigla MPSD. Neste trabalho, entende-se por modificação, a inclusão de um parâmetro na função massa de probabilidade da distribuição Série de Potência tornando essa nova família de distribuições capaz de modelar adequadamente conjunto de dados para os casos em que há excesso (inflação), falta (deflação), ausência ou até mesmo quando a frequência da observação k estiver de acordo para a suposição de uma distribuição Série de Potência. Para esta nova família de distribuições são apresentadas propriedades como Função de distribuição, Função característica, Função geradora de momentos, Estatística de Ordem dentre outras, além de contextualiza-la como modelo de mistura. As distribuições consideradas para a construção dessa nova família serão as distribuições uniparamétricas pertencentes à família Série de Potência, cuja função massa de probabilidade pode ser escrita em função de sua média.
50

Anti-Specker Properties in Constructive Reverse Mathematics

Dent, James Edgar January 2013 (has links)
Constructive reverse mathematics is a programme in which non- and semi-constructive principles are classified in accordance with which other principles they imply or are implied by, relative to the framework of Bishop-style constructive mathematics. One such principle that has come under focus in recent years is an antithesis of Specker's theorem (that theorem being a characteristic result of Russian recursive mathematics): this so-called anti-Specker property is intuitionistically valid, and of considerable utility in proving results of real and complex analysis. We introduce several new weakenings of the anti-Specker property and explore their role in constructive reverse mathematics, identifying implication relationships that they stand in to other notable principles. These include, but are not limited to: variations upon Brouwer's fan theorem, certain compactness properties, and so-called zero-stability properties. We also give similar classification results for principles arising directly from Specker's theorem itself, and present new, direct proofs of related fan-theoretic results. We investigate how anti-Specker properties, alongside power-series-based arguments, enable us to recover information about the structure of holomorphic functions: in particular, they allow us to streamline a sequence of maximum-modulus theorems.

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