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1
Tarbouriech, Cédric. "Avoir une partie 2 × 2 = 4 fois : vers une méréologie des slots". Electronic Thesis or Diss., Toulouse 3, 2023. http://www.theses.fr/2023TOU30316.
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La méréologie est la discipline qui s'intéresse aux relations entre une partie et son tout et entre parties au sein d'un même tout. Selon la théorie la plus communément utilisée, appelée "méréologie classique extensionnelle", une entité ne peut être partie d'une autre entité qu'une seule fois. Par exemple, votre cœur n'est qu'une seule fois partie de votre corps. Ce principe a été remis en question par certains travaux antérieurs. En effet, il n'est pas possible de décrire la structure méréologique de certaines entités, telles que les universaux structurés ou les types de mots, dans le cadre de la méréologique classique extensionnelle. Ces entités peuvent avoir plusieurs fois la même partie. Par exemple, l'universel de molécule d'eau (H2O) a comme partie l'universel d'atome d'hydrogène (H) deux fois, alors qu'une molécule d'eau particulière a comme parties deux atomes d'hydrogène distincts. Dans ce travail, nous suivons la piste ouverte par Karen Bennett en 2013. Bennett a ébauché une nouvelle méréologie qui permette de représenter la structure méréologique de ces entités. Dans sa théorie, être une partie d'une entité, c'est remplir un "slot" de cette entité. Ainsi, dans le mot "patate", la lettre "a" est partie du mot deux fois, parce qu'elle occupe deux "slots" de ce mot : le deuxième et le quatrième. La proposition de Bennett est innovante en cela qu'elle offre un cadre général, qui n'est pas restreint à un type d'entités. Toutefois, la théorie souffre de plusieurs problèmes. D'abord, elle est limitée : de nombreuses notions de méréologie classique n'y ont pas d'équivalent, telles que la somme méréologique ou l'extensionnalité. Ensuite, parce que la théorie, par son axiomatique, provoque des problèmes de comptage. Ainsi, l'universel d'électron n'est partie que sept fois de l'universel de méthane, au lieu des dix fois qui sont attendues. Nous avons proposé une solution dont le principe est que les slots doivent être dupliqués autant de fois que nécessaires pour obtenir un comptage correct. Cette duplication est opérée grâce à un mécanisme appelé "contextualisation", qui permet de copier les slots en rajoutant un contexte supplémentaire. Ainsi, nous avons établi une théorie permettant de représenter des entités qui peuvent avoir plusieurs la même partie tout en évitant les problèmes de comptage. Nous avons développé une méréologie des slots sur la base de cette théorie, c'est-à-dire une théorie représentant des relations méréologiques entre slots. Ainsi, nous avons pu développer les diverses notions présentes en méréologie classique, telles que la supplémentation, l'extensionnalité, la somme et la fusion méréologiques. Cette proposition fournit une méréologie très expressive et logiquement bien fondée qui permettra d'explorer, dans de futurs travaux, des questions complexes soulevées dans la littérature scientifique. En effet, certaines entités ne peuvent pas être différenciées par leurs seules structures méréologiques, mais requièrent de représenter des relations additionnelles entre leurs parties. Notre théorie méréologique offre des outils et des pistes permettant d'explorer de telles questionsMereology is the discipline concerned with the relationships between a part and its whole and between parts within a whole. According to the most commonly used theory, "classical extensional mereology", an entity can only be part of another one once. For example, your heart is part once of your body. Some earlier works have challenged this principle. Indeed, it is impossible to describe the mereological structure of certain entities, such as structural universals or word types, within the framework of classical extensional mereology. These entities may have the same part several times over. For example, the universal of water molecule (H2O) has as part the universal of hydrogen atom (H) twice, while a particular water molecule has two distinct hydrogen atoms as parts. In this work, we follow the track opened by Karen Bennett in 2013. Bennett sketched out a new mereology to represent the mereological structure of these entities. In her theory, to be a part of an entity is to fill a "slot" of that entity. Thus, in the word "potato", the letter "o" is part of the word twice because it occupies two "slots" of that word: the second and the sixth. Bennett's proposal is innovative in offering a general framework that is not restricted to one entity type. However, the theory has several problems. Firstly, it is limited: many notions of classical mereology have no equivalent, such as mereological sum or extensionality. Secondly, the theory's axiomatics give rise to counting problems. For example, the electron universal is only part of the methane universal seven times instead of the expected ten times. We have proposed a solution based on the principle that slots must be duplicated as often as necessary to obtain a correct count. This duplication is achieved through a mechanism called "contextualisation", which allows slots to be copied by adding context. In this way, we have established a theory for representing entities that may have the same part multiple times while avoiding counting problems. We have developed a mereology of slots based on this theory, which is a theory representing mereological relationships between slots. In this way, we have developed the various notions present in classical mereology, such as supplementation, extensionality, mereological sum and fusion. This proposal provides a very expressive and logically sound mereology that will enable future work to explore complex issues raised in the scientific literature. Indeed, some entities cannot be differentiated by their mereological structures alone but require the representation of additional relationships between their parts. Our mereological theory offers tools and avenues to explore such questions
2
Vial, Pierre. "Opérateurs de typage non-idempotents, au delà du lambda-calcul". Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC038/document.
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L'objet de cette thèse est l'extension des méthodes de la théorie des types intersections non-idempotents, introduite par Gardner et de Carvalho, à des cadres dépassant le lambda-calcul stricto sensu.- Nous proposons d'abord une caractérisation de la normalisation de tête et de la normalisation forte du lambda-mu calcul (déduction naturelle classique) en introduisant des types unions non-idempotents. Comme dans le cas intuitionniste, la non-idempotence nous permet d'extraire du typage des informations quantitatives ainsi que des preuves de terminaison beaucoup plus élémentaires que dans le cas idempotent. Ces résultats nous conduisent à définir une variante à petits pas du lambda-mu-calcul, dans lequel la normalisation forte est aussi caractérisée avec des méthodes quantitatives. - Dans un deuxième temps, nous étendons la caractérisation de la normalisation faible dans le lambda-calcul pur à un lambda-calcul infinitaire étroitement lié aux arbres de Böhm et dû à Klop et al. Ceci donne une réponse positive à une question connue comme le problème de Klop. À cette fin, il est nécessaire d'introduire conjointement un système (système S) de types infinis utilisant une intersection que nous qualifions de séquentielle, et un critère de validité servant à se débarrasser des preuves dégénérées auxquelles les grammaires coinductives de types donnent naissance. Ceci nous permet aussi de donner une solution au problème n°20 de TLCA (caractérisation par les types des permutations héréditaires). Il est à noter que ces deux problèmes n'ont pas de solution dans le cas fini (Tatsuta, 2007).- Enfin, nous étudions le pouvoir expressif des grammaires coinductives de types, en dehors de tout critère de validité. Nous devons encore recourir au système S et nous montrons que tout terme est typable de façon non triviale avec des types infinis et que l'on peut extraire de ces typages des informations sémantiques comme l'ordre (arité) de n'importe quel lambda-terme. Ceci nous amène à introduire une méthode permettant de typer des termes totalement non-productifs, dits termes muets, inspirée de la logique du premier ordre. Ce résultat prouve que, dans l'extension coinductive du modèle relationnel, tout terme a une interprétation non vide. En utilisant une méthode similaire, nous montrons aussi que le système S collapse surjectivement sur l'ensemble des points de ce modèleIn this dissertation, we extend the methods of non-idempotent intersection type theory, pioneered by Gardner and de Carvalho, to some calculi beyond the lambda-calculus.- We first present a characterization of head and strong normalization in the lambda-mu calculus (classical natural deduction) by introducing non-idempotent union types. As in the intuitionistic case, non-idempotency allows us to extract quantitative information from the typing derivations and we obtain proofs of termination that are far more elementary than those in the idempotent case. These results leads us to define a small-step variant of the lambda-mu calculus, in which strong normalization is also characterized by means of quantitative methods.- In the second part of the dissertation, we extend the characterization of weak normalization in the pure lambda-calculus to an infinitary lambda-calculus narrowly related to Böhm trees, which was introduced by Klop et al. This gives a positive answer to a question known as Klop's problem. In that purpose, it is necessary to simultaneously introduce a system (system S) featuring infinite types and resorting to an intersection operator that we call sequential, and a validity criterion in order to discard unsound proofs that coinductive grammars give rise to. This also allows us to give a solution to TLCA problem #20 (type-theoretic characterization of hereditary permutations). It is to be noted that those two problem do not have a solution in the finite case (Tatsuta, 2007).- Finally, we study the expressive power of coinductive type grammars, without any validity criterion. We must once more resort to system S and we show that every term is typable in a non-trivial way with infinite types and that one can extract semantical information from those typings e.g. the order (arity) of any lambda-term. This leads us to introduce a method that allows typing totally unproductive terms (the so-called mute terms), which is inspired from first order logic. This result establishes that, in the coinductive extension of the relational model, every term has a non-empty interpretation. Using a similar method, we also prove that system S surjectively collapses on the set of points of this model
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Marais, Magdaleen Suzanne. "Idempotente voortbringers van matriksalgebras". Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/677.
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Blomgren, Martin. "Fibrations and Idempotent Functors". Doctoral thesis, KTH, Matematik (Avd.), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-66740.
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This thesis consists of two articles. Both articles concern homotopical algebra. In Paper I we study functors indexed by a small category into a model category whose value at each morphism is a weak equivalence. We show that the category of such functors can be understood as a certain mapping space. Specializing to topological spaces, this result is used to reprove a classical theorem that classifies fibrations with a fixed base and homotopy fiber. In Paper II we study augmented idempotent functors, i.e., co-localizations, operating on the category of groups. We relate these functors to cellular coverings of groups and show that a number of properties, such as finiteness, nilpotency etc., are preserved by such functors. Furthermore, we classify the values that such functors can take upon finite simple groups and give an explicit construction of such values.QC 20120127
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Yang, Dandan. "Free idempotent generated semigroups". Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/5948/.
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The study of the free idempotent generated semigroup IG$(E)$ over a biordered set $E$ began with the seminal work of Nambooripad in the 1970s and has seen a recent revival with a number of new approaches, both geometric and combinatorial. Given the universal nature of free idempotent generated semigroups, it is natural to investigate their structure. A popular theme is to investigate the maximal subgroups. It was thought from the 1970s that all such groups would be free, but this conjecture was false. The first example of a non-free group arising in this context appeared in 2009 in an article by Brittenham, Margolis and Meakin. After that, Gray and Ru\v{s}kuc in 2012 showed that {\em any} group occurs as a maximal subgroup of some $\ig(E)$. Following this discovery, another interesting question comes out very naturally: for a particular biordered $E$, which groups can be the maximal subgroups of $\ig(E)$? Several significant results for the biordered sets of idempotents of the full transformation monoid $\mathcal{T}_n$ on $n$ generators and the matrix monoid $M_n(D)$ of all $n\times n$ matrices over a division ring $D,$ have been obtained in recent years, which suggest that it may well be worth investigating maximal subgroups of $\ig(E)$ over the biordered set $E$ of idempotents of the endomorphism monoid of an independence algebra of finite rank $n$. To this end, we investigate another important example of an independence algebra, namely, the free (left) $G$-act $F_n(G)$ of rank $n$, where $n\in \mathbb{N}$, $n\geq 3$ and $G$ is a group. It is known that the endomorphism monoid $\en F_n(G)$ of $F_n(G)$ is isomorphic to a wreath product $G\wr \mathcal{T}_n$. We say that the {\em rank} of an element of $\en F_n(G)$ is the minimal number of (free) generators in its image. Let $E$ be the biordered set of idempotents of $\en F_n(G)$, let $\varepsilon\in E$ be a rank $r$ idempotent, where $1\leq r\leq n.$ For rather straightforward reasons it is known that if $r=n-1$ (respectively, $n$), then the maximal subgroup of $\ig(E)$ containing $\varepsilon$ is free (respectively, trivial). We show, in a transparent way, that, if $r=1$ then the maximal subgroup of IG$(E)$ containing $\varepsilon$ is isomorphic to that of $\en F_n(G)$ and hence to $G$. As a corollary we obtain the 2012 result of Gray and Ru\v{s}kuc that {\em any} group can occur as a maximal subgroup of {\em some} $\ig(E)$. Unlike their proof, ours involves a natural biordered set and very little machinery. However, for higher ranks, a more sophisticated approach is needed, which involves the presentations of maximal subgroups of $\ig(E)$ obtained by Gray and Ru\v{s}kuc, and a presentation of $G\wr\mathcal{S}_r$, where $\mathcal{S}_r$ is the symmetric group on $r$ elements. We show that for $1\leq r\leq n-2$, the maximal subgroup of $\ig(E)$ containing $\varepsilon$ is isomorphic to that of $\en F_n(G)$, and hence to $G\wr\mathcal{S}_r$. By taking $G$ to be trivial, we obtain an alternative proof of the 2012 result of Gray and Ru\v{s}kuc for the biordered set of idempotents of $\mathcal{T}_n.$ After that, we focus on the maximal subgroups of $\ig(E)$ containing a rank 1 idempotent $\varepsilon\in E$, where $E$ is the biordered set of idempotents of the endomorphism monoid $\en \mathbf{A}$ of an independence algebra $\mathbf{A}$ of rank $n$ with no constants, where $n\in \mathbb{N}$ and $n\geq 3.$ It is proved that the maximal subgroup of $\ig(E)$ containing $\varepsilon$ is isomorphic to that of $\en \mathbf{A},$ the latter being the group of all unary term operations of $\mathbf{A}.$ Whereas much of the former work in the literature of $\ig(E)$ has focused on maximal subgroups, in this thesis we also study the general structure of the free idempotent generated semigroup $\ig(B)$ over an arbitrary band $B$. We show that $\ig(B)$ is {\it always} a weakly abundant semigroup with the congruence condition, but not necessarily abundant. We then prove that if $B$ is a quasi-zero band or a normal band for which $\ig(B)$ satisfying Condition $(P)$, then $\ig(B)$ is an abundant semigroup. In consequence, if $Y$ is a semilattice, then $\ig(Y)$ is adequate, that is, it belongs to the quasivariety of unary semigroups introduced by Fountain over 30 years ago. Further, the word problem of $\ig(B)$ is solvable if $B$ is quasi-zero. We also construct a 10-element normal band $B$ for which $\ig(B)$ is not abundant.
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Leupold, Klaus-Peter. "Languages Generated by Iterated Idempotencies". Doctoral thesis, Universitat Rovira i Virgili, 2006. http://hdl.handle.net/10803/8791.
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The rewrite relation with parameters m and n and with the possible length limit = k or :::; k we denote by w~, =kW~· or ::;kw~ respectively. The idempotency languages generated from a starting word w by the respective operations are wDOur investigations about idempotency relations and languages start out from the case of a uniform length bound. For these relations =kW~ the conditions for confluence are characterized completely. Also the question of regularity is -k n answered for aH the languages w- D
For a generallength bound, i.e."for the relations :"::kW~, confluence does not hold so frequently. This complicatedness of the relations results also in more complicated languages, which are often non-regular, as for example the languages W<;kD
The concept of root in Formal Language ·Theory is frequently used to describe the reduction of a word to another one, which is in sorne sense elementary.
For example, there are primitive roots, periodicity roots, etc. Elementary in connection with duplication are square-free words, Le., words that do not contain any repetition. Thus we define the duplication root of w to consist of aH the square-free words, from which w can be reached via the relation w~.
Besides sorne general observations we prove the decidability of the question, whether the duplication root of a language is finite.
Then we devise acode, which is robust under duplication of its code words.
This would keep the result of a computation from being destroyed by dupli cations in the code words. We determine the exact conditions, under which infinite such codes exist: over an alphabet of two letters they exist for a length bound of 2, over three letters already for a length bound of 1.
Also we apply duplication to entire languages rather than to single words; then it is interesting to determine, whether regular and context-free languages are closed under this operation. We show that the regular languages are closed under uniformly bounded duplication, while they are not closed under duplication with a generallength bound. The context-free languages are closed under both operations.
The thesis concludes with a list of open problems related with the thesis' topics.
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Lelièvre, Hubert. "Espaces bmo et multiplicateurs idempotents". Paris 6, 1995. http://www.theses.fr/1995PA066372.
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On etudie une generalisation des espaces bmo et des espaces de hardy classiques en remplacant les normes d'espace de lebesgue par des normes d'orlicz dans les definitions. Notre but, ensuite, c'est la generalisation de l'inegalite classique de paley dans le cas des fonctions a valeurs aussi bien scalaires que vectorielles. Cela nous permet de mettre en evidence des sous-espaces de fonctions, remarquables engendres par des suites lacunaires. Par la methode d'interpolation de peetre, on calcule des espaces intermediaires entre l'espace bmo et l'espace des fonctions essentiellement bornees. La derniere partie de la these est consacree aux multiplicateurs idempotents sur des espaces de type bmo
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Sezinando, Helena Maria da Encarnação. "Formal languages and idempotent semigroups". Thesis, University of St Andrews, 1991. http://hdl.handle.net/10023/13724.
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The structure of the lattice LB of varieties of idempotent semigroups or bands (as universal algebras) was determined by Birjukov, Fennemore and Gerhard. Wis- math determined the structure of a related lattice: the lattice LBM of varieties of band monoids. In the first two parts we study several questions about these varieties. In Part I we compute the cardinalities of the Green classes of the free objects in each variety of LB [LBM]. These cardinalities constitute a useful piece of information in the study of several questions about these varieties and some of the conclusions obtained here are used in parts II and III. Part II concerns expansions of bands [band monoids]. More precisely, we compute here the cut-down to generators of the Rhodes expansions of the free objects in the varieties of LB. We define Rhodes expansion of a monoid, its cut-down to generators and we compute the cut-down to generators of the Rhodes expansions of the free objects in the varieties of LBM. In Part III we deal with Eilenberg varieties of band monoids. The last chapter is particularly concerned with the description of the varieties of languages corresponding to these varieties.
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Garcia, Vitor Araujo. "Idempotentes centrais primitivos em algumas álgebras de grupos". Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05102015-225032/.
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O objetivo do trabalho é apresentar alguns resultados acerca de anéis de grupos e aplicações, segundo o que foi estudado em livros e artigos sobre o assunto. Inicialmente, apresentaremos alguns fatos básicos sobre anéis de grupos, que podem ser encontrados em [5], e em seguida, apresentaremos os resultados principais, mais recentes, que foram estudados em dois artigos diferentes. No primeiro artigo [4], apresentou-se uma forma de calcular o número de componentes simples de certas álgebras de grupos abelianos finitos, bem como também foi apresentada uma forma de calcular geradores idempotentes de códigos abelianos minimais, suas dimensões e seus pesos. No segundo artigo [2], encontra-se uma descrição feita dos idempotentes centrais primitivos da álgebra de grupo racional de grupos nilpotentes finitos.Our goal in this project is to present some results about group rings and its applications, as presented in books and articles about this subject. First of all we are going to establish some basic fact about group rings, which can be found mainly in [5], and then we will present the main results, which are more recent, and have been studied in two different articles. In [4], the authors presented a way of evaluating the number of simple components of some finite group algebras, as well presented a way of evaluating idempotent generators of some minimal abelian codes, their dimension and their weights. In [2] there is a complete description of all the primitive central idempotents of the rational group algebra of finite nilpotent groups.
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Krautzberger, Peter [Verfasser]. "Idempotent filters and ultrafilters / Peter Krautzberger". Berlin : Freie Universität Berlin, 2009. http://d-nb.info/1023817063/34.
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Deshpande, Ameet Shridhar. "Efficient idempotent methods for optimal control". Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3389391.
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Thesis (Ph. D.)--University of California, San Diego, 2009.Title from first page of PDF file (viewed February 12, 2010). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 178-182).
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Hunter, Andrew. "An investigation of idempotents in nest algebras". Thesis, University of Leeds, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328919.
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Michalski, Burkhard. "On the lattice of varieties of almost-idempotent semirings". Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2018. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-232529.
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Die Arbeit beschäftigt sich mit fast-idempotenten Halbringen, die eine Verallgemeinerung der idempotenten Halbringe darstellen. Es werden - ausgehend von Halbringen mit zwei Elementen - bis auf isomorphe Bilder sämtliche fast-idempotente Halbringe mit drei Elementen generiert, diejenigen Halbringe, die schon in durch zweielementige Halbringe erzeugten Varietäten liegen, aussortiert und die in den verbleibenden elf Halbringen gültigen Gleichungen charakterisiert. Der Verband L(IA3) der Varietäten generiert durch fast-idempotente Halbringe mit maximal drei Elementen wird mit Hilfe eines Kontexts mit 21 Halbringen als Attribute und 28 trennenden Gleichungen als Objekte vollständig bestimmt und besteht aus 19.901 Varietäten. Im Anschluss richtet sich der Fokus der Arbeit auf den Verband L(IA) der fast-idempotenten Halbringe. In diesem werden insbesondere die Varietät V = [xy = yx, xy = xy+x] und deren Untervarietäten V_k = [x^k = x^(k+1)], k >= 2; untersucht. Für all diese Varietäten wird jeweils eine Konstruktionsmethode für eine abzählbare Kette an Untervarietäten der gegebenen Varietät eingeführt und somit schließlich gezeigt, dass der Verband L(IA) aus mindestens abzählbar unendlich vielen Varietäten besteht.
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Cathcart, Alan George. "Maps between spectra and the Steinberg idempotent". Thesis, University of Cambridge, 1988. https://www.repository.cam.ac.uk/handle/1810/250924.
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Heider, Blaise J. "Annihilators and Extensions of Idempotent Generated Ideals". Thesis, University of Louisiana at Lafayette, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=10808908.
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We define a ring R to be right cP-Baer if the right annihilator of a cyclic projective right R-module is generated by an idempotent. We also define a ring R to be right I-extending if each ideal generated by an idempotent is right essential in a direct summand of R. It is shown that the two conditions are equivalent in a semiprime ring. Next we define a right I-prime ring, which generalizes the prime condition. This condition is equivalent to all cyclic projective right R-modules being faithful. For a semiprime ring, we show the existence of a cP-Baer hull. We also provide some results about the p.q.-Baer hull and when it is equal to the cP-Baer hull. Polynomial and formal power series rings are studied with respect to the right cP-Baer condition. In general, a formal power series ring over one indeterminate in which its base ring is right p.q.-Baer ring is not necessarily right p.q.-Baer. However, if the base ring is right cP-Baer then the formal power series ring over one indeterminate is right cP-Baer. The fifth chapter is devoted to matrix extensions of right cP-Baer rings. A characterization of when a 2-by-2 generalized upper triangular matrix ring is right cP-Baer is given. The last major theorem is a decomposition of a cP-Baer ring, satisfying a finiteness condition, into a generalized triangular matrix ring with right I-prime rings down the main diagonal. Examples illustrating and delimiting our results are provided.
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Poncet, Paul. "Analyse idempotente en dimension infinie : le rôle des ensembles ordonnés continus". Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00666633.
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L'analyse idempotente étudie les espaces linéaires de dimension infinie dans lesquels l'opération maximum se substitue à l'addition habituelle. Nous démontrons un ensemble de résultats dans ce cadre, en soulignant l'intérêt des outils d'approximation fournis par la théorie des domaines et des treillis continus. Deux champs d'étude sont considérés : l'intégration et la convexité. En intégration idempotente, les propriétés des mesures maxitives à valeurs dans un domaine, telles que la régularité au sens topologique, sont revues et complétées ; nous élaborons une réciproque au théorème de Radon-Nikodym idempotent ; avec la généralisation Z de la théorie des domaines nous dépassons différents travaux liés aux représentations de type Riesz des formes linéaires continues sur un module idempotent. En convexité tropicale, nous obtenons un théorème de type Krein-Milman dans différentes structures algébriques ordonnées, dont les semitreillis et les modules idempotents topologiques localement convexes ; pour cette dernière structure nous prouvons un théorème de représentation intégrale de type Choquet : tout élément d'un compact convexe K peut être représenté par une mesure de possibilité supportée par les points extrêmes de K. Des réflexions sont finalement abordées sur l'unification de l'analyse classique et de l'analyse idempotente. La principale piste envisagée vient de la notion de semigroupe inverse, qui généralise de façon satisfaisante à la fois les groupes et les semitreillis. Dans cette perspective nous examinons les propriétés "miroir" entre semigroupes inverses et semitreillis, dont la continuité fait partie. Nous élargissons ce point de vue en conclusion.
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Nemo, Clémentine. "Construction et validation de modèles guidées par l'application idempotente de transformations". Nice, 2010. http://www.theses.fr/2010NICE4090.
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Les systèmes d’information d’entreprise (SIE) visent à mettre à disposition des développeurs un ensemble d’éléments hétérogènes (politiques, composants sur étagère, patrons de conception,…) communs à tous les projets de l’entreprise. Le développement des logiciels se fait ainsi par l’alternance d’intégrations des briques logicielles et de modifications manuelles des codes. Lorsque les briques logicielles correspondent à l’introduction de politiques, telle que le contrôle d’accès, les assemblages de composants résultants respectent les contraintes imposées par la politique. Or, l’intégration d’autres politiques et les modifications de l’utilisateur peuvent violer ces contraintes et introduire des incohérences dans le modèle. Assurer et éventuellement établir la cohérence des assemblages construits par introductions de politiques est la problématique abordée par ce travail de thèse. Dans cette thèse, nous appréhendons une politique comme une transformation de modèle à modèle où son application, par des propriétés d’idempotence, modifie uniquement les éléments de modélisation nécessaires. Nous proposons alors une spécification des transformations afin de définir par construction des transformations idempotentes que nous nommons ITC. Cette formalisation consiste à spécifier la sémantique des actions élémentaires composant l’expression d’une ITC à spécifier le processus d’application d’une ITC. Les applications d’ITCs deviennent alors la base pour construite, valider et réparer un modèle. Nous définissons alors un algorithme de rejeu d’un ensemble d’applications d’ITCs afin de construire un modèle validant un ensemble de contraintes liées à un ensemble de politiques. L’écriture de l’expression des ITCs à partir d’actions élémentaires, l’application des ITCs et l’algorithme de rejeu sont mises en œuvre dans un moteur d’applications implémenté en Prolog. Nous illustrons cette contribution à travers une étude de cas où nous mettons en avant la nécessité de permettre les introductions séquentielles et ensemblistes des politiquesModel transformations play a critical role in Model Driven Development because they automate recurrent software development tasks. Some of these transformations are refinement of models by adding or retracting elements to produce new models conforming to additional constraints. For example, such transformations are used to integrate non functional properties. But modifications of the resulting model can break the conformity to those functional properties. Our challenge is to detect and restore this conformity applying the same transformation again. In this thesis, we defend that model transformation is the key concept to validate and restore models and we establish a system to define idempotent transformations
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Assis, Ailton Ribeiro de. "Idempotentes em Álgebras de Grupos e Códigos Abelianos Minimais". Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7401.
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Previous issue date: 2011-09-09Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work, we study the semisimple group algebras FqCn of the finite abelian groups Cn over a finite field Fq and give conditions so that the number of its simple components is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. Under such conditions, we compute the set of primitive idempotents of FqCn and from there, we study the abelian codes as minimal ideals of the group algebra, which are generated by the primitive idempotents, computing their dimension and minimum distances.
Neste trabalho, estudamos álgebras de grupos semisimples FqCn de grupos abelianos finitos Cn sobre um corpo finito Fq e as condições para que o número de componentes simples seja mínimo, ou seja igual ao número de componentes simples sobre a álgebra de grupos racionais do mesmo grupo. Sob tais condições, calculamos o conjunto de idempotentes primitivos de FqG e a de partir daí, estudamos os códigos cíclicos como ideais minimais da álgebra de grupo, os quais são gerados pelos idempotentes primitivos, calculando suas dimensões e distâncias mínimas.
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Garba, Goje Uba. "Idempotents, nilpotents, rank and order in finite transformation semigroups". Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/13703.
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Ondrusch, Nicole. "Komplexitäts- und Entscheidbarkeitsresultate für inverse Monoide mit idempotenter Präsentation". [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-28589.
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Lewin, Andrew Michael. "Idempotent generated subsemigroups of endomorphism monoids of universal algebras". Thesis, University of York, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280427.
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Poncet, Paul. "Infinite-dimensional idempotent analysis : the role of continuous posets". Palaiseau, Ecole polytechnique, 2011. https://pastel.hal.science/docs/00/66/66/33/PDF/thesisPONCET20120205.pdf.
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"L'analyse idempotente étudie les espaces linéaires de dimension infinie dans lesquels l'opération maximum se substitue à l'addition habituelle. Nous démontrons un ensemble de résultats dans ce cadre, en soulignant l'intérêt des outils d'approximation fournis par la théorie des domaines et des treillis continus. Deux champs d'étude sont considérés : l'intégration et la convexité. En intégration idempotente, les propriétés des mesures maxitives à valeurs dans un domaine, telles que la régularité au sens topologique, sont revues et complétées ; nous élaborons une réciproque au théorème de Radon-Nikodym idempotent ; avec la généralisation Z de la théorie des domaines nous dépassons différents travaux liés aux représentations de type Riesz des formes linéaires continues sur un module idempotent. En convexité tropicale, nous obtenons un théorème de type Krein-Milman dans différentes structures algébriques ordonnées, dont les semitreillis et les modules idempotents topologiques localement convexes ; pour cette dernière structure nous prouvons un théorème de représentation intégrale de type Choquet : tout élément d'un compact convexe K peut être représenté par une mesure de possibilité supportée par les points extrêmes de K. Des réflexions sont finalement abordées sur l'unification de l'analyse classique et de l'analyse idempotente. La principale piste envisagée vient de la notion de semigroupe inverse, qui généralise de façon satisfaisante à la fois les groupes et les semitreillis. Dans cette perspective nous examinons les propriétés "miroir" entre semigroupes inverses et semitreillis, dont la continuité fait partie. Nous élargissons ce point de vue en conclusion"Idempotent analysis involves the study of infinite-dimensional linear spaces in which the usual addition is replaced by the maximum operation. We prove a series of results in this framework and stress the crucial contribution of domain and continuous lattice theory. Two themes are considered: integration and convexity. In idempotent integration, the properties of domain-valued maxitive measures such as regularity are surveyed and completed in a topological framework; we provide a converse statement to the idempotent Radon-Nikodym theorem; using the Z generalization of domain theory we gather and surpass existing results on the representation of continuous linear forms on an idempotent module. In tropical convexity, we obtain a Krein-Milman type theorem in several ordered algebraic structures, including locally-convex topological semilattices and idempotent modules; in the latter structure we prove a Choquet integral representation theorem: every point of a compact convex subset K can be represented by a possibility measure supported by the extreme points of K. The hope for a unification of classical and idempotent analysis is considered in a final step. The notion of inverse semigroup, which fairly generalizes both groups and semilattices, may be the right candidate for this; in this perspective we examine "mirror" properties between inverse semigroups and semilattices, among which continuity. The general conclusion broadens this point of view
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Aiston, Anna Katherine. "Skein theoretic idempotents of Hecke algebras and quantum group invariants". Thesis, University of Liverpool, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307662.
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Megzari, Saïd. "Idempotents dans les algebres de clifford et fibrations spinorielles amorphes". Toulouse 3, 1986. http://www.theses.fr/1986TOU30146.
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L'objet de ce travail est la definition et l'etude des fibrations spinorielles amorphes sur une variete pseudo-riemannienne; sous fibres en ideaux a gauche minimaux du fibre de clifford, ces fibrations n'ont ete introduites que plus recemment par le professeur a. Crumeyrolle. On donne des conditions necessaires et suffisantes de leur existence qui se traduisent par la possibilite de reduire le groupe orthogonal a un groupe de spinorialite orthogonal. Tenant compte du fait que toute anti-involution gamma peut s'ecrire sous la forme gamma =beta oh ou h est un automorphisme on donne une caracterisation des anti-involutions commutant avec l'action d'un sous-groupe h de g en particulier lorsque h=g on trouve beta et beta. On montre aussi lorsqu'on a une reduction du groupe orthogonal 0(p,q) a 0(p) qui equivaut a l'existence de l'anti-involution tenant compte de la signature que pour tout ideal a gauche minimal de c::(p,q) (n=p+q pair) ou de c::(p,q) n impair. Il existe un idempotent primitif particulier et une anti-involution laissant cet idempotent invariant et commutant avec l'action d'un sous-groupe du groupe de clifford, associe a cet idempotant et qui intervient dans le probleme de reduction. L'existence de ces fibrations n'est pas reliee aux proprietes intrinseques de la variete, elles dependent du choix de l'idempotent engendrant la fibretype, ceci explique pourquoi les champs d'idempotents primitifs ne sont pas en general une bonne methode pour definir les fibrations spinorielles amorphes.
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Megzari, Saïd. "Idempotents dans les algèbres de Clifford et fibrations spinorielles amorphes". Grenoble 2 : ANRT, 1986. http://catalogue.bnf.fr/ark:/12148/cb37599572g.
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Yu, Hoseog. "Idempotent relations and the conjecture of Birch and Swinnerton-Dyer /". The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488190595940334.
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Bastos, Gustavo Terra. "Comparação de técnicas para o de idempotentes geradores de códigos abelianos". Universidade Federal de Viçosa, 2013. http://www.locus.ufv.br/handle/123456789/7928.
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Neste trabalho, desenvolvemos um estudo de técnicas polinomial e de álgebra de grupo de grupos abelianos para o cálculo de idempotentes primitivos em anéis semissimples, sob certas hipóteses. Estes idempotentes primitivos podem ser vistos como geradores de códigos abelianos minimais. Apresentamos resultados recentes para ambas as técnicas e, a partir de exemplos, realizamos um estudo comparativo das mesmas. Nesta comparação, identificamos possíveis erros na técnica polinomial abordada e propomos as devidas correções para o caso de códigos de comprimento p n q, utilizando ambas as abordagens para a demonstração do resultado correto.
In this work, under certain hypotheses, we study two techniques for the computation of primitive idempotents in semissimple rings, namely, the polynomial and the group algebra techniques, the latter for abelian groups. These primitive idempotents can be seen as generator idempotents of minimal abelian codes. We present recent results for both techniques and, with examples, we compare them. In this comparison, we identify possible errors in the polynomial technique and we propose the corrections for the case of codes of length p n q, using the both approaches to prove the correct result.
Dissertação não estava cadastrada no TEDE
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Torii, Takeshi. "Level structure over E^n and stable splitting by Steinberg idempotent". 京都大学 (Kyoto University), 1999. http://hdl.handle.net/2433/181444.
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Bernadet, Alexis. "Non idempotent-intersection types to refine strong normalisation with quantitative information". Palaiseau, Ecole polytechnique, 2014. https://tel.archives-ouvertes.fr/tel-01099657/document.
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Nous étudions des systèmes de typage avec des types intersections non-idempotents pour des variantes du lambda-calcul et nous discutons de leurs propriétés et de leurs applications. Outre le lambda-calcul lui-même, les variantes sont un lambda-calcul avec des substitutions explicites et un lambda-calcul avec des constructeurs, du filtrage et un opérateur de point fixe. Les sytèmes de typage que l'on présente caractérisent les termes fortement normalisables. Mais nous montrons également qu'un jugement de typage d'un terme donne des informations quantitatives : une mesure triviale sur l'arbre de typage d'unlambda-terme quelconque donne une borne sur la taille de la plus longue séquence de beta-reductions depuis ce lambda-terme jusqu'à sa forme normale. Nous raffinons cette approche pour obtenir un résultat plus précis: certains systèmes de typages, sous certaines conditions, donnent même une mesure exacte de cette plus longue séquence de beta-reductions, et le type du terme donne des informations sur la forme normale de ce terme. De plus, en utilisant des filtres, ces systèmes de typage peuvent être utilisés pour définir une sémantique dénotationnelleWe study systems of non-idempotent intersection types for different variants of the lambda-calculus and we discuss properties and applications. Besides the pure lambda-calculus itself, the variants are a λ-calculus with explicit substitutions and a lambda-calculus with constructors, matching and a fixpoint operator. The typing systems we introduce for these calculi all characterize strongly normalising terms. But we also show that, by dropping idempotency of intersections, typing a term provides quantitative information about it: a trivial measure on its typing tree gives a bound on the size of the longest beta-reduction sequence from this term to its normal form. We explore how to refine this approach to obtain finer results: some of the typing systems, under certain conditions, even provide the exact measure of this longest beta-reduction sequence, and the type of a term gives information on the normal form of this term. Moreover, by using filters, these typing systems can be used to define a denotational semantics
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Gardiner, Sean Bruce Gilbert. "On maximal subgroups of idempotent-generated semigroups associated with biordered sets". Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25481.
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Given any biordered set $E$, we may form the idempotent-generated semigroup $F_E$, which is generated by the set $E$, subject to the relations $ef=e*f$ whenever $e$ and $f$ are elements of $E$ and $e*f$ is a basic product. Easdown proved in 1985 that the biordered set of $F_E$ is biorder isomorphic to $E$, thus demonstrating that the biordered set axioms, introduced by Nambooripad in 1974, characterise certain partial algebras of idempotents of semigroups. Relatively little is known about the general structure of $F_E$, though it is known that every group can arise as a maximal subgroup of $F_E$ for some $E$, and that, as a consequence, the word problem is unsolvable. We provide a presentation of the maximal subgroups associated with a given $\mathcal{D}$-class of $F_E$, which is based on establishing relators that arise from singular squares that are located throughout the graph $\Gamma$ of the $\mathcal{D}$-class. We further apply this machinery to several classes of small examples.
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Loreaux, Jireh. "Diagonals of Operators: Majorization, a Schur-Horn Theorem and Zero-Diagonal Idempotents". University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1470753493.
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Mandhapati, Venkata Srikanth y Kamran Ali Bajwa. "Evaluation of Idempotency & Block Size of Data on the Performance of Normalized Compression Distance Algorithm". Thesis, Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-4303.
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Normalized compression distance (NCD) is a similarity distance metric algorithm which is used for the purpose of analyzing the type of file fragments. The performance of NCD depends upon underlying compression algorithm to be used. We have studied three compressors bzip2, gzip and ppmd, the compression ratio of ppmd is better than bzip2 and the compression ratio of bzip2 is better than gzip, but which one out of these three is better than one another in the viewpoint of idempotency is evaluated by us. Then we have applied NCD along with k nearest neighbour as a classification algorithm to a randomly selected public corpus data with different block sizes (512 byte, 1024 bytes, 1536 bytes, 2048 bytes). The performance of two compressors bzip2 and gzip is also compared for the NCD algorithm in the perspective of idempotency. Objectives: In this study we have investigated the In this study we have investigated the combine effect of both of the parameters namely compression ratio versus idempotency and varying block size of data on the performance of NCD. The objective is to figure out that in order to have a better performance of NCD either a compressor for NCD should be selected on the basis of better compression ratio of compressors or better idempotency of compressors. The whole purpose of using different block sizes was to evaluate either the performance of NCD will improve or not by varying the block size of data to be used for making the datasets. Methods: Experiments are performed to test the hypotheses and evaluate the effect of compression ratio versus idempotency and block size of data on the performance of NCD. Results: The results obtained after the analysis of null hypotheses of main experiment are retained, which showed that there is no statistically significant difference on the performance of NCD when varying block size of data is used and also there is no statistically significant difference on the NCD’s performance when a compressor is selected for NCD on the basis of better compression ratio or better idempotency. Conclusions: As the results obtained from the experiments are unable to reject the null hypotheses of main experiment so no conclusion could be drawn of the effect of the independent variables on the dependent variable i.e. there is no statistically significant effect of compression ratio versus idempotency and varying block size of data on performance of the NCD.
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Borchers, Brian Edward. "Uniquely clean elements, optimal sets of units and counting minimal sets of units". Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1829.
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Let R be a ring. We say x ∈ R is clean if x = e + u where u is a unit and e is an idempotent (e2 = e). R is clean if every element of R is clean. I will give the motivation for clean rings, which comes from Fitting's Lemma for Vector Spaces. This leads into the ABCD lemma, which is the foundation of a paper by Camillo, Khurana, Lam, Nicholson and Zhou. Semi-perfect rings are a well known type of ring. I will show a relationship that occurs between clean rings and semi-perfect rings which will allow me to utilize what is known already about semi-perfect rings. It is also important to note that I will be using the Fundamental Theorem of Torsion-free Modules over Principal Ideal Domains to work with finite dimensional vector spaces. These finite dimensional vector spaces are in fact strongly clean, which simply means they are clean and the idempotent and unit commute. This additionally means that since L = e + u, Le = eL. Several types of rings are clean, including a weaker version of commutative Von Neumann regular rings, Duo Von Neumann regular, which I have proved. The goal of my research is to find out how many ways to write matrices or other ring elements as sums of units and idempotents. To do this, I have come up with a method that is self contained, drawing from but not requiring the entire literature of Nicholson. We also examine sets other than idempotents such as upper-triangular and row reduced and examine the possibility or exclusion that an element may be represented as the sum of a upper-triangular (resp. row reduced) element and a unit. These and other element properties highlight some of the complexity of examining an additive property when the underlying properties are multiplicative.
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Bendaoud, Zohra. "Comportement à l'origine de la distance entre éléments d'un semigroupe fortement continu et inégalités dans les algèbres de Banach". Bordeaux 1, 2008. http://www.theses.fr/2008BOR13549.
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Le but de cette thèse est, d'une part d'étudier certaines inégalités valables dans les algèbres de Banach ne possédant aucun idempotent non nul, et d'autre part d'expliciter des idempotents dans les algèbres de Banach ne vérifiant pas ces inégalités. On obtient des inégalités de ce type concernant la norme de et la norme de pour γ > 0. On améliore également la condition de Esterle-Mokhtari concernant la norme de condition qui permet de conclure qu'un semi-groupe admet une limite en norme à l'origine, quand est un entier. On donne enfin des formules explicites permettant de construire une suite exhaustive d'idempotents dans l'algèbre de Banach engendrée par un semi-groupe fortement continu ne vérifiant pas la minoration au voisinage de l'origine.
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Tomlin, Drew E. "A Decomposition of the Group Algebra of a Hyperoctahedral Group". Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc955102/.
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The descent algebra of a Coxeter group is a subalgebra of the group algebra with interesting representation theoretic properties. For instance, the natural map from the descent algebra of the symmetric group to the character ring is a surjective algebra homomorphism, so the descent algebra implicitly encodes information about the representations of the symmetric group. However, this property does not hold for other Coxeter groups. Moreover, a complete set of primitive idempotents in the descent algebra of the symmetric group leads to a decomposition of the group algebra as a direct sum of induced linear characters of centralizers of conjugacy class representatives. In this dissertation, I consider the hyperoctahedral group. When the descent algebra of a hyperoctahedral group is replaced with a generalization called the Mantaci-Reutenauer algebra, the natural map to the character ring is surjective. In 2008, Bonnafé asked whether a complete set of idempotents in the Mantaci-Reutenauer algebra could lead to a decomposition of the group algebra of the hyperoctahedral group as a direct sum of induced linear characters of centralizers. In this dissertation, I will answer this question positively and go through the construction of the idempotents, conjugacy class representatives, and linear characters required to do so.
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Ibanez, Elsa. "Idempotents de Jones-Wenzl évaluables aux racines de l'unité et représentation modulaire sur le centre de U¯_{q}sl(2)". Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS233.
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Soit p∈ℕ*. On définit une famille d'idempotents (et de nilpotents) des algèbres de Temperley-Lieb aux racines 4p-ième de l'unité qui généralise les idempotents de Jones-Wenzl usuels. Ces nouveaux idempotents sont associés aux représentations simples et indécomposables projectives de dimension finie du groupe quantique restreint U¯_{q}sl(2), où q est une racine 2p-ième de l'unité. A l'instar de la théorie des champs quantique topologique (TQFT) de [BHMV95], ils fournissent une base canonique de classes d'écheveaux coloriés pour définir des représentations des groupes de difféotopie des surfaces. Dans le cas du tore, cette base nous permet d'obtenir une correspondance partielle entre les actions de la vrille négative et du bouclage, et la représentation de SL₂(ℤ) de [LM94] induite sur le centre de U¯_{q}sl(2), qui étend non trivialement de la représentation de SL₂(ℤ) obtenue par la TQFT de [RT91]Let p in N^*. We define a family of idempotents (and nilpotents) in the Temperley-Lieb algebras at 4p-th roots of unity which generalizes the usual Jones-Wenzl idempotents. These new idempotents correspond to finite dimentional simple and projective indecomposable representations of the restricted quantum group U¯_{q}sl(2), where q is a 2p-th root of unity. In the manner of the [BHMV95] topological quantum field theorie (TQFT), they provide a canonical basis in colored skein modules to define mapping class groups representations. In the torus case, this basis allows us to obtain a partial match between the negative twist and the buckling actions, and the [LM94] induced representation of SL₂(ℤ) on the center of U¯_{q}sl(2), which extends non trivially the [RT91] representation of SL₂(ℤ)
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Lahaye, Sébastien. "Contributions à l'étude des systèmes à événements discrets à partir de modèles définis sur des semi-anneaux idempotents". Habilitation à diriger des recherches, Université d'Angers, 2011. http://tel.archives-ouvertes.fr/tel-00841440.
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Ce manuscrit a été rédigé en vue d'obtenir l'habilitation à diriger des recherches. J'y présente mon implication dans l'enseignement supérieur et la recherche au sein de l'Université d'Angers depuis mon recrutement en tant que maître de conférences, et plus précisément en tant qu'enseignant à l'ISTIA et en tant que chercheur au LISA. Au LISA, dirigé par Jean-Louis Ferrier au moment de mon recrutement, j'ai intégré l'équipe Modèles et Systèmes Dynamiques. Mon travail de recherche a profité des interactions avec les différents membres de cette équipe, et en particulier avec Jean-Louis Boimond (comme le laisseront apparaître les références dans la suite de ce manuscrit). Il concerne le comportement temporisé des systèmes à événements discrets en utilisant des modèles définis sur une structure algébrique de semi-anneau idempotent, encore appelée dioïde. Le document est structuré de la manière suivante. - Le premier chapitre présente mon curriculum vitae ainsi qu'un survol général de mes activités de recherche. - Le deuxième chapitre fait une synthèse plus détaillée de travaux motivés par deux préoccupations principales durant ces onze dernières années : élargir la classe des modèles relevant de la théorie des systèmes sur l'algèbre des dioïdes ; appliquer les résultats de la théorie des systèmes sur les dioïdes à l'analyse des systèmes de transport. En annexe, trois publications sont jointes pour que le lecteur puisse trouver plus de détails sur ces travaux. - Dans le troisième et dernier chapitre, je tire un bilan et envisage des perspectives à mes travaux.
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Cossu, Laura. "Factorizations of invertible matrices into products of elementary matrices and of singular matrices into products of idempotent matrices". Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3426221.
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In this thesis we consider two classical problems, originated respectively by a 1966 paper by P. Cohn and by a 1967 one by J.A. Erdos, concerning the factorization of square matrices with entries in an arbitrary domain: we want to characterize integral domains R satisfying property
(GEn), every n x n invertible matrix over R is a product of elementary matrices;
and those satisfying property
(IDn), every n x n singular matrix over R is a product of idempotent matrices.
There is a deep relationship between properties (GEn) and (IDn). An important result by Ruitenburg (1993) shows that they are equivalent for Bézout domains (i.e. integral domains whose finitely generated ideals are principal).
Moreover, if R is a Bézout domain, then R satisfies (GEn) for any n≥2 if and only if it satisfies (GE2) if and only if it satisfies (ID2) if and only if it satisfies (IDn) for any n≥2. Thus, in this case, it is enough to consider matrices of dimension 2.
The thesis investigates two conjectures, as natural as hard to prove in general. The first one, due to Salce and Zanardo (2014) and suggested by important results on number fields, is the following: "a principal ideal domain R satisfies the property (ID2) if and only if it is Euclidean". In support of this conjecture, in this thesis we prove that it is valid in two important classes of non-Euclidean PID's: (i) the coordinate rings of special
non-singular algebraic curves defined over a perfect field k, among them the coordinate rings of conics without k-rational points and the coordinate rings of elliptic curves having the point at infinity as unique k-rational point; (ii) the class of non-Euclidean PID's constructed by D.D. Anderson in a
1988 paper. The cases (i) and (ii) require different proofs, based on delicate technical lemmas. From these results we get that the conjecture seems to be verified by every non-Euclidean PID appeared in the literature.
The second conjecture studied in this thesis is related to the factorization of singular matrices into idempotent ones: "an integral domain R verifying (GE2) must be a Bézout domain".
Unique factorization domains, projective-free domains and PRINC domains, introduced by Salce and Zanardo in 2014, satisfy the conjecture. In the thesis we exhibit an example of PRINC domain which is neither UFD nor projective-free. We also prove that if an integral domain R satisfies the property (ID2), then it is a Prüfer domain (i.e. finitely generated ideals of R are invertible); thus in order to study the second conjecture we can confine ourselves to the class of Prüfer domains. Moreover, we show that if any integral domain R satisfies property (ID2), then it satisfies also property (GE2). Using this result and properly applying some results by Cohn (1996), in support of the conjecture we find a class of coordinate rings of smooth algebraic curves that are not PID's and that do not satisfy property (ID2); moreover we prove that also the ring Int(Z) of integer-valued polynomials does not
verify this property.In questa tesi si considerano due problemi classici, originati rispettivamente da un lavoro di P. Cohn del 1966 e da uno di J.A. Erdos del 1967, inerenti la fattorizzazione di matrici quadrate a coefficienti in un arbitrario dominio di integrità: caratterizzare i domini di integrità R che soddisfano la proprietà (GEn), ogni matrice invertibile n x n a valori in R è prodotto di matrici elementari; e quelli che soddisfano la proprietà (IDn), ogni matrice singolare n x n a valori in R è prodotto di matrici idempotenti. Vi è una stretta correlazione tra le proprietà (GEn) e (IDn). Un importante risultato di Ruitenburg (1993) mostra che esse sono equivalenti nei domini di Bézout (cioè domini integrali in cui ogni ideale finitamente generato è principale). Inoltre, se R è un dominio di Bézout, allora R soddisfa (GEn) per ogni n≥2 se e solo se vale la (GE2), se e solo se vale la (ID2), se e solo se verifica la (IDn) per ogni n≥2. In questo caso è quindi sufficiente considerare le matrici di dimensione 2. La trattazione si sviluppa attorno allo studio di due congetture, tanto naturali quanto difficili da dimostrare in generale. La prima, proposta da Salce e Zanardo (2014) e ispirata da importanti risultati sui campi di numeri algebrici, è la seguente: "un dominio a ideali principali R soddisfa la proprieta (GE2) se e solo se è Euclideo". A supporto di tale congettura, nella tesi viene dimostrata la sua validità in due importanti classi di PID non Euclidei: (i) gli anelli delle coordinate di speciali curve algebriche non singolari definite su un campo perfetto k, tra cui l'anello delle coordinate delle coniche prive di punti razionali su k e quello delle curve ellittiche aventi il punto all'infinito come unico punto razionale; (ii) i PID non Euclidei costruiti da D.D. Anderson in un lavoro del 1988. I casi (i) e (ii) richiedono differenti dimostrazioni, basate su delicati lemmi tecnici. Da tali risultati si evince che la congettura sembra essere verificata da tutti i PID non Euclidei apparsi in letteratura. La seconda congettura studiata nella tesi è legata alla fattorizzazione di matrici singolari in idempotenti: "un dominio R avente la proprietà (ID2) deve essere necessariamente un dominio di Bézout". I domini a fattorizzazione unica, quelli projective-free, e i domini PRINC, introdotti da Salce e Zanardo nel 2014, soddisfano la congettura. Nella tesi si è trovato un esempio di dominio PRINC che non è né UFD né projective-free. Si è inoltre provato che se un dominio R soddisfa la proprietà (ID2), allora R è un dominio di Prüfer (i.e. gli ideali finitamente generati sono invertibili); la seconda congettura può essere quindi studiata limitandosi alla classe dei domini di Prüfer. Si è dimostrato che se un qualunque dominino di integrità R verifica la proprietà (ID2), allora verifica anche la (GE2). Utilizzando tale risultato e applicando opportunamente differenti risultati di Cohn (1966), a sostegno della congettura si è trovata una classe di anelli coordinati di curve non singolari che sono domini di Dedekind non PID che non soddisfano la proprietà (ID2); si è inoltre provato che neanche l'anello Int(Z) dei polinomi a valori interi verifica tale proprietà.
39
Harrat, Ayoub. "Problème de moments avec applications et estimations du spectre discret des opérateurs définis par des matrices infinies non bornées THE QUINTIC COMPLEX MOMENT PROBLEM ASYMPTOTIC EXPANSION OF LARGE EIGENVALUES FOR A CLASS OF UNBOUNDED JACOBI MATRICES". Thesis, Littoral, 2020. http://www.theses.fr/2020DUNK0563.
Texto completoResumen
Dans cette thèse on donne d'abord une solution concrète pour presque tous les scénarios qu'on peut avoir dans le problème de moments complexe quintique et en particulier dans le cas d'une mesure à support minimal. On présente aussi de nombreux exemples pour illustrer chaque cas. La seconde partie présente une approche qui permet de passer du problème de moments tronqué au problème complet à l'aide des idempotents. Il s'agit d'une approche très différente de celle utilisée dans la première partie.Plus précisément, au lieu d'appliquer les méthodes de R. Curto et L. Fialkow où l'objet central est la matrice de moments, on utilise l'approche de F. Vasilescu dont l'objet central est la fonctionnelle de Riesz. Cette fonctionnelle fait associer à chaque monôme tᵅ la valeur γ∝ et elle satisfait trois conditions naturelles dans le cas où la suite (γ∝)∝∈ℕᵈ est donnée par les intégrales de tᵅ par rapport à une mesure. La troisième partie est consacrée à l'asymptotique du spectre pour une classe de matrices hermitiennes tridiagonales infinies. Le but est d'obtenir le comportement asymptotique précis des valeurs propres y associées à partir du comportement asymptotique de ces coefficients. Le résultat est obtenu par une approche nouvelle qui est une adaptation de la théorie de perturbations de Schrieffer-Wolff utilisée en physique de la matière condensée. Cette méthode marche également pour des matrices 'bande', mais le cas des matrices tridiagonales est le plus important pour des applications et encore les expressions explicites des premières corrections dans la formule asymptotique sont plus simples pour les matrices tridiagonalesIn this thesis, we first provide a concrete solution to the, almost all, quintic TCMP (that is, when m = 5). We also study the cardinality of the minimal representing measure. Based on the bi-variate recurrence sequence properties with some Curto-Fialkow's results. Our method intended to be useful for all odd-degree moment problems. Second, we investigate the full moment problem for discrete measures using Vasilescu's idempotent approach based on Λ-multiplicative elements with respect to the associated square positive Riesz functional. We give a sufficient condition for the existence of a discrete integral representation for the associated Riesz functional, which turns to be necessary in bounded shift space case. A particular attention is given to Λ-multiplicative elements, where a total description, for the cases where they are a single point indicator functions, is given. Lastly, We investigate a class of infinite Jacobi matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly. This method works in general for band matrices but Jacobi matrices case still much interesting due to applications and explicit expressions obtained for the first correction terms in the asymptotic formula
40
Michalski, Burkhard [Verfasser], Udo [Akademischer Betreuer] Hebisch, Udo [Gutachter] Hebisch y Bernhard [Gutachter] Ganter. "On the lattice of varieties of almost-idempotent semirings / Burkhard Michalski ; Gutachter: Udo Hebisch, Bernhard Ganter ; Betreuer: Udo Hebisch". Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2018. http://d-nb.info/1221070088/34.
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Fogarty, Neville Lyons. "On Skew-Constacyclic Codes". UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/36.
Texto completoResumen
Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non-commutative skew-polynomial rings. We introduce a skew-generalized circulant matrix to aid in examining skew-constacyclic codes, and we use it to recover a well-known result on the duals of skew-constacyclic codes from Boucher/Ulmer in 2011. We also motivate and develop a notion of idempotent elements in these quotient modules. We are particularly concerned with the existence and uniqueness of idempotents that generate a given submodule; we generalize relevant results from previous work on skew-constacyclic codes by Gao/Shen/Fu in 2013 and well-known results from the classical case.
42
Varro, Richard. "Algèbres de Bernstein périodiques". Montpellier 2, 1992. http://www.theses.fr/1992MON20256.
Texto completoResumen
Dans le but de modéliser des populations dont la composition génétique suit une succession cyclique d'états d'équilibre, nous présentons une généralisation de la notion d'algèbre de Bernstein d'ordre n en introduisant la notion de périodicité. Nous nous sommes intéressés aux conditions d'existence d'idempotents généralisés et à leurs propriétés, à la structure vectorielle qui apparaît lors de la décomposition de Peierce et à des problèmes de transport de structures dans la dupliquée de ces algèbres. Enfin nous étudions les algèbres qui modelisent les populations d'organismes soumises seulement à la mutation des gènes et nous établissons la condition nécessaire et suffisante pour que ces populations atteignent à la première génération une situation d'équilibre périodique
43
Zhang, Haonan. "Some problems in noncommutative analysis". Thesis, Bourgogne Franche-Comté, 2019. http://www.theses.fr/2019UBFCD043.
Texto completoResumen
Cette thèse de doctorat est consacrée à l'étude de quelques problèmes en analyse non commutative. Elle comprend quatre parties, allant des groupes quantiques et de l'analyse harmonique non commutative à l'information quantique. Tout d'abord, nous déterminons les états idempotents sur les groupes quantiques de Sekine, ce qui est obtenu en résolvant un système d'équations à l'aide de l'algèbre linéaire et de la théorie des nombres élémentaire. Ceci répond à une question de Franz et Skalski énoncée en 2009. Deuxièmement, nous étudions les états infiniment divisibles sur des groupes quantiques finis, c'est-à-dire, les états qui admettent une racine n-ième pour tout nge 1. Nous montrons que tout état infiniment divisible sur un groupe quantique fini est de type Poisson, c'est-à-dire qu'il peut être représenté sous la forme d'une exponentielle par rapport à un état idempotent. Troisièmement, nous donnons deux conditions suffisantes pour que les multiplicateurs de Fourier de L_p sur les algèbres de von Neumann de groupes discrets soient bornés. Très peu de résultats de ce type étaient connus auparavant. Notre idée est l'observation que, dans le cas discret, il suffit de considérer les multiplicateurs de Fourier de L_p-L_q. Enfin, dans le domaine de l'information quantique, nous confirmons une conjecture de Carlen, Frank et Lieb (puis une conjecture plus faible d'Audenaert et Datta). En conséquence, nous identifions toutes les paires (alpha, z) telles que l'alpha-z entropie relative de Rényi soit monotone sous l'action des applications complètement positives préservant la trace, ou satisfait à l'inégalité de traitement des données. La clé de la preuve est une modification d'une méthode variationnelle largement utilisée, qui permet d'obtenir des preuves simples de nombreux résultats connusThis PhD thesis is devoted to the study of some problems in noncommutative analysis. It consists of four parts, ranging from quantum groups and noncommutative harmonic analysis to quantum information. Firstly, we decide all the idempotent states on Sekine quantum groups, which is achieved by solving a system of equations using linear algebras and elementary number theory. This answers a question of Franz and Skalski stated in 2009. Secondly, we study the infinitely divisible states on finite quantum groups, i.e., states that admit n-th root for all nge 1. We show that every infinitely divisible state on a finite quantum group is of Poisson type, that is, it can be represented as an exponential relative to some idempotent state. Thirdly, we give two sufficient conditions for boundedness of L_p-Fourier multipliers on discrete group von Neumann algebras. Very few of such results were known before. Our idea is the observation that in the discrete case it suffices to consider L_p-L_q Fourier multipliers. Finally, in the area of quantum information, we confirm a conjecture of Carlen, Frank and Lieb (and then a weaker conjecture of Audenaert and Datta). As a consequence, we identify all the pairs (alpha,z) such that the alpha-z Rényi relative entropy is monotone under completely positive trace preserving maps, or satisfies Data Processing Inequality. The key part of the proof is a modification of a widely-used variational method. Its power yields simple proofs of many known results
44
Koppen, Vincent Oliver Verfasser] y Christoph [Akademischer Betreuer] [Schweigert. "Hopf-algebraic structures inspired by Kitaev models : defects, comodule algebras and idempotents for non-semisimple Hopfalgebras / Vincent Oliver Koppen ; Betreuer: Christoph Schweigert". Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1214811817/34.
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Koppen, Vincent Oliver [Verfasser] y Christoph [Akademischer Betreuer] Schweigert. "Hopf-algebraic structures inspired by Kitaev models : defects, comodule algebras and idempotents for non-semisimple Hopfalgebras / Vincent Oliver Koppen ; Betreuer: Christoph Schweigert". Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1214811817/34.
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46
PUIG, DE DIOS YUNIED. "RECURRENCE IN LINEAR DYNAMICS". Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/264143.
Texto completoResumen
A bounded and linear operator is said to be hypercyclic if there
exists a vector such that its orbit under the action of the operator
is dense. The first example of a hypercyclic operator on a
Banach space was given in 1969 by Rolewicz who gave conditions for the unweighted unilateral backward shift on l2 to be hypercyclic. Among its features, we
can mention for example that finite-dimensional spaces cannot
support hypercyclic operators, proved by Kitai. On the
other hand, several people have shown in different contexts, in
the Hilbert space frame, that the set of hypercyclic vectors for
a hypercyclic operator is a G dense set.
This thesis is divided into four chapters. In the first one, we give
some preliminaries by mentioning some definitions and known
results that will be of great help later.
In chapter 2, we introduce a refinement of the notion of hypercyclicity,
relative to the set N(U; V ) when belonging to a certain collection F of subsets of N,
namely a bounded and linear operator T is called F-operator
if N(U; V ) belongs to F, for any pair of non-empty open sets U; V in X. First, we do an analysis of the hierarchy established between
F-operators, whenever F covers those families mostly studied
in Ramsey theory. Second, we investigate which kind of properties
of density can the sets N(x;U) and
N(U; V ) have for a given hypercyclic operator, and classify the
hypercyclic operators accordingly to these properties.
In chapter three, we introduce the following notion: an operator
T on X satisfies property PF if for any U non-empty open set in
X, there exists x in X such that N(x;U) belongs to F. Let BD the collection
of sets in N with positive upper Banach density. We generalize
the main result of a recent paper of Costakis and Parissis using a strong result of Bergelson
and Mccutcheon in the vein of Szemerédi’s theorem, leading
us to a characterization of those operators satisfying property
PBD. It turns out that operators having property PBD satisfy a
kind of recurrence described in terms of essential idempotents of
N (the Stone-Cech compactification of N). We will discuss the
case of weighted backward shifts satisfying property PBD. On
the other hand, as a consequence we obtain a characterization
of reiteratively hypercyclic operators, i.e. operators for which
there exists x in X such that for any U non-empty open set in
X, the set N(x;U) belongs to BD.
The fourth chapter focuses on a refinement of the notion of disjoint
hypercyclicity. We extend a result of Bès, Martin, Peris
and Shkarin by stating: a weighted backward shift Bw is F-operator if
and only if (Bw; ... ;Bw^r) is d-F, for any r in N, where F runs along some filters strictly containing the family of cofinite sets,
which are frequently used in Ramsey theory. On the other hand,
we point out that this phenomenon does not occur beyond the
weighted shift frame by showing a mixing linear operator T on
a Hilbert space such that the tuple (T; T^2) is not d-syndetic.
We also, investigate the relationship between reiteratively hypercyclic
operators and d-F tuples, for filters F contained in
the family of syndetic sets. Finally, we examine conditions to
impose in order to get reiterative hypercyclicity from syndeticity
in the weighted shift frame.
47
Puig, de Dios Yunied. "Recurrence in Linear Dynamics". Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/48473.
Texto completoResumen
A bounded and linear operator is said to be hypercyclic if there exists a
vector such that its orbit under the action of the operator is dense. The first
example of a hypercyclic operator on a Banach space was given in 1969 by
Rolewicz who showed that if B is the unweighted unilateral backward shift
on l
2
, then λB is hypercyclic if and only if |λ| > 1. Among its features,
we can mention for example that finite-dimensional spaces cannot support
hypercyclic operators, proved by Kitai. On the other hand, several people
have shown in different contexts, in the Hilbert space frame, that the set of
hypercyclic vectors for a hypercyclic operator is a Gδ dense set.
This thesis is divided into four chapters. In the first one, we give some
preliminaries by mentioning some definitions and known results that will be
of great help later.
In chapter 2, we introduce a refinement of the notion of hypercyclicity,
relative to the set N(U, V ) = {n ∈ N : T
−nU ∩ V 6= ∅} when belonging
to a certain collection F of subsets of N, namely a bounded and linear
operator T is called F-operator if N(U, V ) ∈ F, for any pair of non-empty
open sets U, V in X. First, we do an analysis of the hierarchy established
between F-operators, whenever F covers those families mostly studied in
Ramsey theory. Second, we investigate which kind of properties of density
can have the sets N(x, U) = {n ∈ N : T
nx ∈ U} and N(U, V ) for a given
hypercyclic operator, and classify the hypercyclic operators accordingly to
these properties.
In chapter three, we introduce the following notion: an operator T on
X satisfies property PF if for any U non-empty open set in X, there exists
x ∈ X such that N(x, U) ∈ F. Let BD the collection of sets in N with positive
upper Banach density. We generalize the main result of a paper due to
Costakis and Parissis using a strong result of Bergelson and Mccutcheon in
the vein of Szemerédi’s theorem, leading us to a characterization of those operators
satisfying property PBD. It turns out that operators having property
PBD satisfy a kind of recurrence described in terms of essential idempotents
of βN (the Stone-Čech compactification of N). We will discuss the case of
weighted backward shifts satisfying property PBD. On the other hand, as
a consequence we obtain a characterization of reiteratively hypercyclic operators,
i.e. operators for which there exists x ∈ X such that for any U
non-empty open set in X, the set N(x, U) ∈ BD.
The fourth chapter focuses on a refinement of the notion of disjoint hypercyclicity.
We extend a result of Bès, Martin, Peris and Shkarin by stating:
Bw is F-weighted backward shift if and only if (Bw, . . . , Br
w) is d-F, for any
r ∈ N, where F runs along some filters containing strictly the family of cofi-
nite sets, which are frequently used in Ramsey theory. On the other hand,
we point out that this phenomenon does not occur beyond the weighted shift
frame by showing a mixing linear operator T on a Hilbert space such that the
tuple (T, T2
) is not d-syndetic. We also, investigate the relationship between
reiteratively hypercyclic operators and d-F tuples, for filters F contained
in the family of syndetic sets. Finally, we examine conditions to impose in
order to get reiterative hypercyclicity from syndeticity in the weighted shift
frame.Puig De Dios, Y. (2014). Recurrence in Linear Dynamics [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48473
TESIS
48
Lee, Gangyong. "Theory of Rickart Modules". The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281542099.
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Dressayre-Nourigat, Michelle. "Etude des ω-PI algèbres de degré 4". Montpellier 2, 2008. http://www.theses.fr/2008MON20160.
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Teh, Wen Chean. "Ramsey Algebras and Ramsey Spaces". The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115.
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