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Carrillo-Rouse, Paulo Roberto. "Indices analytiques à support compact pour des groupoïdes de Lie." Paris 7, 2007. http://www.theses.fr/2007PA077160.
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Pour un groupoïde de Lie on construit un morphisme d'indice analytique à valeurs dans un « bon quotient« du groupe de K-théorie de l'algèbre des fonctions à support compact sur le groupoïde. Cet indice est intermédiaire entre l'indice purement algébrique et l'indice analytique à valeurs dans la K-théorie de la C ̂*-algèbre associée au groupoïde. L'avantage de ces indices est que pour les groupes de K-théorie du type support compact on dispose d'un accouplement avec la cohomologie cyclique qui permet d'obtenir des invariants numériques. En particulier on montre que l'accouplement de l'indice d'un G-opérateur elliptique avec un cocycle cyclique périodique est toujours donné au niveau de la classe du symbole principal. La construction des indices à support compact est basée, comme pour le cas C ̂*-algèbre, sur le groupoïde tangent de Connes. En effet, on a été menés à construire une algèbre des fonctions lisses sur le groupoïde tangent qui réalise une déformation entre l'algèbre de convolution du groupoïde de base et l'algèbre de Schwartz de l'algébroïde. On retrouve finalement des formules d'indice de Connes, Connes-Moscovici et Benameur-Heitsch, mais d'une façon purement algébriqueFor a Lie groupoid we construct an analytic index morphism taking values in a « good quotient« of the K-theory group of the algebra of compactly supported functions over the groupoid. This index is intermediate between the purely algebraic index and the analytic index in the K-theory of the C ̂*-algebra. The advantage of these indices is that for the K-theory groups like the compactly supported we have a pairing with the Cyclic cohomology that allow to obtain numerical invariants. In particular we show that the pairing of a G-elliptic operator with a periodic cyclic cocycle is always given at the level of the principal symbol class. The construction of our indices is also based, as in the C ̂*-algebra case, in the Connes tangent groupoid. Indeed, we had to construct an algebra of smooth functions over the tangent groupoid that performs a deformation between the convolution algebra of the base groupoid on the Schwartz algebra of the Lie algebroid. We finally found some index formulas by Connes, Connes-Moscovici and Benameur-Heitsch, but in a purely algebraic way
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Carrillo, Rouse Paulo. "Indices analytiques à support compact pour des groupoïdes de Lie." Phd thesis, Université Paris-Diderot - Paris VII, 2007. http://tel.archives-ouvertes.fr/tel-00271219.
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Pour un groupoïde de Lie, on construit un morphisme d'indice analytique à valeurs dans un certain quotient de la K-théorie de l'algèbre de convolution de fonctions lisses à support compact. La construction est aboutie grâce à l'introduction d'une algèbre de déformation de fonctions lisses sur le groupoïde tangent. Ceci permet en particulier de montrer une version plus primitive du théorème de l'indice longitudinal de Connes-Skandalis for Foliations, c'est à dire, un théorème de l'indice qui prend ses valeurs dans un groupe qui peut être accouplé avec des cocycles cycliques. Une autre application est la suivante: soit D un G-opérateur pseudodifférential eliiptique avec indice ind(D)€K_0(A) (où A est l'algèbre de convolution), alors l'accouplement de ind(D) avec un coycle cyclique borné ne dépend que de la classe du symbole principal de D. Ce résultat est général pour des goupoïdes étale.
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Cellini, Caroline Paula. "Dualidade de Poincaré e invariantes cohomológicos /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/99831.
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Orientador: Ermínia de Lourdes Campello FantiBanca: Fernanda Soares Pinto Cardona
Banca: Maria Gorete Carreira Andrade
Resumo: Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos "ends" e grupos de dualidade são apresentados.
Abstract: In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant "ends" and duality groups are presented.
Mestre
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Cellini, Caroline Paula [UNESP]. "Dualidade de Poincaré e invariantes cohomológicos." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/99831.
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cellini_cp_me_sjrp.pdf: 781641 bytes, checksum: 70ed1b385d132f8255370c0014be09b4 (MD5)Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos ends e grupos de dualidade são apresentados.
In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant ends and duality groups are presented.
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Rajhi, Anis. "Cohomologie d'espaces fibrés au-dessus de l'immeuble affine de GL(N)." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2266/document.
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Cette thèse se compose de deux parties : dans la première on donne une généralisation d'espaces fibrés construit au-dessus de l'arbre de Bruhat-Tits du groupe GL(2) sur un corps p-adique. Plus précisément, on a construit une tour projective d'espaces fibrés au-dessus du 1-squelette de l'immeuble de Bruhat-Tits de GL(n) sur un corps p-adique. On a montré que toute représentation cuspidale π de GL(n) se plonge avec multiplicité 1 dans le premier espace de cohomologie à support compact du k-ième étage de la tour, où k est le conducteur de π. Dans la deuxième partie on a construit un espace W au-dessus de la subdivision barycentrique de l'immeuble de Bruhat-Tits de GL(n) sur un corps p-adique. Pour étudier les espaces de cohomologie à support compact d'un G-complexe simplicial propre X muni d'un recouvrement équivariant assez particulier, où G est un groupe localement compact totalement discontinu, on a montré l'existence d'une suite spactrale dans la catégorie des représentations lisses de G qui converge vers la cohomologie à support compact de X. En s'appuyant sur ce dernier résultat, on a calculé la cohomologie à support compact de l'espace W comme représentation lisse de GL(n) puis on a montrer que les types cuspidaux de niveau 0 de GL(n) apparaissent avec multiplicité fini dans la cohomologie de certain complexes fini construit au niveau résiduel. Comme conséquence, on montre que les représentations cuspidales de niveau 0 de GL(n) apparaissent dans la cohomologie de WThis thesis consists of two parts: the first one gives a generalization of fiber spaces constructed above the Bruhat-Tits tree of the group GL(2) over a p-adic field. More precisely we construct a projective tower of spaces over the 1-skeleton of the Bruhat-Tits building of GL(n) over a p-adic field. We show that any cuspidal representation π of GL(n) embeds with multiplicity 1 in the first cohomology space with compact support of k-th floor of the tower, where k is the conductor of π. In the second part we constructed a space W above the barycentric subdivision of the Bruhat-Tits building of GL(n) over a p-adic field. To study the cohomology spaces with compact support of a proper G-simplicial complex X with a rather special equivariant covering, where G is a totally disconnected locally compact group, we show the existence of a spactrale sequence in the category of smooth representations of G that converges to the cohomology with compact support of X. Based on the latter results, we calculate the cohomology with compact support of W as smooth representation of GL(n), and then we show that the level zero cuspidal types of GL(n) appear with finite multiplicity in the cohomology of some finite simplicial complexes constructed in residual level. As a consequence, we show that the cuspidal representations of level 0 of GL(n) appear in the cohomology of W
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Limoges, Thierry. "Structures produits sur la filtration par le poids des variétés algébriques réelles." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4001/document.
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On associe à chaque variété algébrique définie sur R un complexe de cochaînes filtré, qui calcule la cohomologie à supports compacts et coefficients dans Z_2 de ses points réels. Ce complexe filtré est additif pour les inclusions fermées et acyclique pour la résolution des singularités, et est unique à quasi-isomorphisme filtré près. Il est représenté par la filtration duale de la filtration géométrique sur les chaînes semi-algébriques à supports fermés définie par McCrory and Parusiński, et induit une suite spectrale qui calcule la filtration par le poids sur la cohomologie à supports compacts. Cette suite spectrale est un invariant naturel qui contient les nombres de Betti virtuels. On montre que le produit cartésien de deux variétés nous permet de comparer le produit de leurs complexe de poids et suite spectrale respectifs avec ceux du produit, et on prouve que les produits cap et cup en cohomologie et homologie sont filtrés par rapport à ces filtrations par le poids réellesWe associate to each algebraic variety defined over R a filtered cochain complex, which computes the cohomology with compact supports and Z_2-coefficients of the set of its real points. This filtered complex is additive for closed inclusions and acyclic for resolution of singularities, and is unique up to filtered quasi-isomorphism. It is represented by the dual filtration of the geometric filtration on semialgebraic chains with closed supports defined by McCrory and Parusiński, and leads to a spectral sequence which computes the weight filtration on cohomology with compact supports. This spectral sequence is a natural invariant which contains the additive virtual Betti numbers. We then show that the cross product of two varieties allows us to compare the product of their respective weight complexes and spectral sequences with those of their product, and prove that the cup and cap products in cohomology and homology are filtered with respect to the real weight filtrations
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Bergh, Petter Andreas. "Hochschild cohomology, complexity and support varieties." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1491.
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This PhD-thesis consists of the five papers
- On the Hochschild (co)homology of quantum exterior algebras, to appear in Comm. Algebra,
-Complexity and periodicity, Coll. Math. 104 (2006), no. 2, 169-191,
-Twisted support varieties,
-Modules with reducible complexity, to appear in J. Algebra,
- On support varieties for modules over complete intersections, to appear in Proc. Amer. Math. Soc.
These papers are roughly divided into two groups; the ¯rst three study modules over Artin algebras using techniques from Hochschild cohomology, whereas the last two papers study modules over commutative Noetherian local rings, in particular modules over complete intersections.
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Bletz-Siebert, Oliver. "Homogeneous spaces with the cohomology of sphere products and compact quadrangles." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966590341.
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馮淑貞 and Suk-ching Fung. "Asymptotic vanishing theorem of cohomology groups on compact quotientsof the unit ball." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31220848.
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Fung, Suk-ching. "Asymptotic vanishing theorem of cohomology groups on compact quotients of the unit ball /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20667991.
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Fukumoto, Yoshiyasu. "On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes." Kyoto University, 2016. http://hdl.handle.net/2433/217729.
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Sarria, Luis Alberto Alba. "On local cohomology and local homology based on an arbitrary support." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9246.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work develops the theories of local cohomology and local homology with respect to an arbitrary set of ideals and generalises most of the important results from the classical theories. It also introduces the category of quasi-holonomic D-modules and proves some finiteness properties of local cohomology modules which generalise Lyubeznik's results in some sense.
Este trabalho desenvolve as teorias de cohomologia e homologia locais com respeito a um conjunto arbitrário de ideais e generaliza vários dos resultados importantes das teorias clássicas. Também, introduz a categoria dos D-módulos quase-holônomos e prova alguns resultados de finitude de cohomologia local que generalizam, em algum sentido, os resultados de G. Lyubeznik.
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Ignatyev, Oleksiy. "The Compact Support Property for Hyperbolic SPDEs: Two Contrasting Equations." [Kent, Ohio] : Kent State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=kent1216323351.
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Thesis (Ph. D.)--Kent State University, 2008.Title from PDF t.p. (viewed Nov. 10, 2009). Advisor: Hassan Allouba. Keywords: stochastic partial differential equations; compact support property. Includes bibliographical references (p. 30).
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Istrati, Nicolina. "Conformal structures on compact complex manifolds." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC054/document.
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Dans cette thèse on s’intéresse à deux types de structures conformes non-dégénérées sur une variété complexe compacte donnée. La première c’est une forme holomorphe symplectique twistée (THS), i.e. une deux-forme holomorphe non-dégénérée à valeurs dans un fibré en droites. Dans le deuxième contexte, il s’agit des métriques localement conformément kähleriennes (LCK). Dans la première partie, on se place sur un variété de type Kähler. Les formes THS généralisent les formes holomorphes symplectiques, dont l’existence équivaut à ce que la variété admet une structure hyperkählerienne, par un théorème de Beauville. On montre un résultat similaire dans le cas twisté, plus précisément: une variété compacte de type kählerien qui admet une structure THS est un quotient fini cyclique d’une variété hyperkählerienne. De plus, on étudie sous quelles conditions une variété localement hyperkählerienne admet une structure THS. Dans la deuxième partie, les variétés sont supposées de type non-kählerien. Nous présentons quelques critères pour l’existence ou non-existence de métriques LCK spéciales, en terme du groupe de biholomorphismes de la variété. En outre, on étudie le problème d’irréductibilité analytique des variétés LCK, ainsi que l’irréductibilité de la connexion de Weyl associée. Dans un troisième temps, nous étudions les variétés LCK toriques, qui peuvent être définies en analogie avec les variétés de Kähler toriques. Nous montrons qu’une variété LCK torique compacte admet une métrique de Vaisman torique, ce qui mène à une classification de ces variétés par le travail de Lerman. Dans la dernière partie, on s’intéresse aux propriétés cohomologiques des variétés d’Oeljeklaus-Toma (OT). Plus précisément, nous calculons leur cohomologie de de Rham et celle twistée. De plus, on démontre qu’il existe au plus une classe de de Rham qui représente la forme de Lee d’une métrique LCK sur un variété OT. Finalement, on détermine toutes les classes de cohomologie twistée des métriques LCK sur ces variétésIn this thesis, we are concerned with two types of non-degenerate conformal structures on a given compact complex manifold. The first structure we are interested in is a twisted holomorphic symplectic (THS) form, i.e. a holomorphic non-degenerate two-form valued in a line bundle. In the second context, we study locally conformally Kähler (LCK) metrics. In the first part, we deal with manifolds of Kähler type. THS forms generalise the well-known holomorphic symplectic forms, the existence of which is equivalent to the manifold admitting a hyperkähler structure, by a theorem of Beauville. We show a similar result in the twisted case, namely: a compact manifold of Kähler type admitting a THS structure is a finite cyclic quotient of a hyperkähler manifold. Moreover, we study under which conditions a locally hyperkähler manifold admits a THS structure. In the second part, manifolds are supposed to be of non-Kähler type. We present a few criteria for the existence or non-existence for special LCK metrics, in terms of the group of biholomorphisms of the manifold. Moreover, we investigate the analytic irreducibility issue for LCK manifolds, as well as the irreducibility of the associated Weyl connection. Thirdly, we study toric LCK manifolds, which can be defined in analogy with toric Kähler manifolds. We show that a compact toric LCK manifold always admits a toric Vaisman metric, which leads to a classification of such manifolds by the work of Lerman. In the last part, we study the cohomological properties of Oeljeklaus-Toma (OT) manifolds. Namely, we compute their de Rham and twisted cohomology. Moreover, we prove that there exists at most one de Rham class which represents the Lee form of an LCK metric on an OT manifold. Finally, we determine all the twisted cohomology classes of LCK metrics on these manifolds
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Belogay, Eugene Alexandrov. "Construction of smooth orthogonal wavelets with compact support in R[superscript d]." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/28826.
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Adjogah, Benedict E. "Are Highly Dispersed Variables More Extreme? The Case of Distributions with Compact Support." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2382.
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We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.
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Amellaoui, Abdelkebir. "Ondelettes splines à support compact sur une grille irrégulière et approximations numériques stables." Paris 11, 1996. http://www.theses.fr/1996PA112422.
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Le travail de cette thèse constitue une réponse à la conjecture de F. Plantevin (thèse de l'université de Provence, 1992). En observant le phénomène de Gibbs que présente la solution numérique de l'équation de Burgers et la nature de la grille des points représentant les coefficients non négligeables de cette solution, F. Plantevin s'est proposée de construire des ondelettes adaptatives à une telle grille lui permettant de construire une transformée en ondelettes rapide et des algorithmes numériquements stables d'analyse et de synthèse. Pour cause de non invariance par translation et dilatation, le problème de la stabilité n'a pu être résolu. L'alternative que nous présentons à cette construction est basée sur une idée totalement différente: on utilise la technique de commutation entre projecteurs des analyses multi-résolutions bi-orthogonales. Nous avons donc construit une suite d'analyses multi-résolutions sur une grille irrégulière telle que les projecteurs vérifient la propriéte importante de dérivation et primitivation des analyses multi-résolutions bi-orthogonales. Les ondelettes qui découlent de notre construction sont des fonctions splines à support compact. L'invariance par translation et dilatation du problème nous permet d'appliquer le lemme des vaguelettes pour obtenir des estimations dans les espaces fonctionnels et de démontrer la stabilité des algorithmes d'analyse et de synthèse qui découlent de notre construction. Nous avons aussi démontré l'invariance par translation et dilatation des interpolantes de F. Plantevin à partir desquelles nous avons construit les bases duales de nos analyses multi-resolutions. Finalement, nous avons développé et testé les algorithmes d'analyse et de synthèse pour le traitement des singularités.
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Ayache, Antoine. "Bases multivariées d'ondelettes, orthonormales, non séparables, à support compact et de régularité arbitraire." Paris 9, 1997. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1997PA090046.
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Une base d'ondelettes orthonormales dyadiques de L#2 (R#D) est une base hilbertienne de la forme 2#J#D#/#2#I(2#JX K)/ I , 1,, 2#D 1, J , Z et K , Z#D, elle est en général associée à une analyse multi résolution et à un banc de filtres. On ne savait pas encore construire des ondelettes mères #I non séparables, à support compact et de régularité quelconque, (une ondelette séparable est un produit d'ondelette(s) et de fonction(s) d'échelle monodimensionnelles). L'objectif de cette thèse est d'analyser et de résoudre ce problème. Nous établissons d'abord, au moyen d'outils de géométrie algébrique, que la plupart des analyses multi résolution dont le QMF est d'une taille donnée sont non séparables. Nous construisons ensuite, par des calculs assez simples, de nouveaux bancs de filtres, le plus souvent non séparables. Nous montrons enfin que certains de ces bancs de filtres engendrent des bases d'ondelettes de I#2 (R#D), dyadiques, orthonormales, non séparables, à support compact et de régularité arbitrairement élevée.
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Werner, Nils [Verfasser], Gerald [Akademischer Betreuer] Schuller, and Bernd [Gutachter] Edler. "Lapped Nonuniform Orthogonal Transforms with Compact Support / Nils Werner ; Gutachter: Bernd Edler ; Betreuer: Gerald Schuller." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2021. http://d-nb.info/1237499178/34.
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Henriksson, Michael. "A Cognitive Work Analysis as Basis for Development of a Compact C2 System to Support Air Surveillance Work." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-181614.
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This Master of Science thesis is producedat SAAB Security and Defence Solutions.The purpose of the thesis is to analyzehow air surveillance work can be carriedout. This information is then used to givesuggestions for the design of a new systemcontaining only the most essentialfunctionality. This is done by examiningthe available frameworks which can informinterface design and applying a frameworkto analyze work in a complete system usedas the basis of the new Compact C2 system.The second part of the analysis isdirected towards the stripped system(Compact C2) and both parts of theanalysis are used to inform interfacedesign of the Compact C2 system. By usingthe full range of the chosen framework foranalysis of the identification process inSwedish air surveillance work, someessential functions were identified andshould also have support in a Compact C2 system.
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Lasserre, Sébastien. "Contribution à l' étude mathématique et numérique des solutions à support compact pour les modèles de turbulence compressible." Paris 6, 2005. http://www.theses.fr/2005PA066427.
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Sauvy, Paul. "Étude de quelques problèmes elliptiques et paraboliques quasi-linéaires avec singularités." Thesis, Pau, 2012. http://www.theses.fr/2012PAUU3020/document.
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Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles non-linéaires. Plus précisément, nous avons fait ici l’étude de problèmes quasi-linéaires singuliers. Le terme "singulier" fait référence à l’intervention d’une non-linéarité qui explose au bord du domaine où ’équation est posée. La présence d’une telle singularité entraîne un manque de régularité et donc de compacité des solutions qui ne nous permet pas d’appliquer directement les méthodes classiques de l’analyse non-linéaire pour démontrer l’existence de solutions et discuter des propriétés de régularité et de comportement asymptotique de ces solutions. Pour contourner cette difficulté, nous sommes amenés à établir des estimations a priori très fines au voisinage du bord du domaine en combinant diverses méthodes : méthodes de monotonie (reliée au principe du maximum), méthodes variationnelles, argument de convexité, méthodes de point fixe et semi-discrétisation en temps. A travers, l’étude de trois problèmes-modèle faisant intervenir l’opérateur p-Laplacien, nous avons montré comment ces différentes méthodes pouvaient être mises en œuvre. Les résultats que nous avons obtenus sont décrits dans les trois chapitres de cette thèse : Dans le Chapitre I, nous avons étudié un problème d’absorption elliptique singulier. En utilisant des méthodes de sur- et sous solutions et des méthodes variationnelles, nous établissons des résultats d’existence de solutions. Par des méthodes de comparaison locale, nous démontrons également la propriété de support compact de ces solutions, pour de fortes singularités. Dans le Chapitre II, nous étudions le cas d’un système d’équations quasi-linéaires singulières. Par des arguments de point fixe et de monotonie, nous démontrons deux résultats généraux d’existence de solutions. Dans un deuxième temps, nous faisons une analyse plus détaillée de systèmes du type Gierer-Meinhardt modélisant des phénomènes biologiques. Des résultats d’unicité ainsi que des estimations précises sur le comportement des solutions sont alors obtenus. Dans le Chapitre III, nous faisons l’étude d’un problème d’absorption, parabolique singulier. Nous établissons par une méthode de semi-discrétisation en temps des résultats d’existence de solutions. Grâce à des inégalités d’énergie, nous démontrons également l’extinction en temps fini de ces solutionsThis thesis deals with the mathematical field of nonlinear partial differential equations analysis. More precisely, we focus on quasilinear and singular problems. By singularity, we mean that the problems that we have considered involve a nonlinearity in the equation which blows-up near the boundary. This singular pattern gives rise to a lack of regularity and compactness that prevent the straightforward applications of classical methods in nonlinear analysis used for proving existence of solutions and for establishing the regularity properties and the asymptotic behavior of the solutions. To overcome this difficulty, we establish estimations on the precise behavior of the solutions near the boundary combining several techniques : monotonicity method (related to the maximum principle), variational method, convexity arguments, fixed point methods and semi-discretization in time. Throughout the study of three problems involving the p-Laplacian operator, we show how to apply this different methods. The three chapters of this dissertation the describes results we get :– In Chapter I, we study a singular elliptic absorption problem. By using sub- and super-solutions and variational methods, we prove the existence of the solutions. In the case of a strong singularity, by using local comparison techniques, we also prove that the compact support of the solution. In Chapter II, we study a singular elliptic system. By using fixed point and monotonicity arguments, we establish two general theorems on the existence of solution. In a second time, we more precisely analyse the Gierer-Meinhardt systems which model some biological phenomena. We prove some results about the uniqueness and the precise behavior of the solutions. In Chapter III, we study a singular parabolic absorption problem. By using a semi-discretization in time method, we establish the existence of a solution. Moreover, by using differential energy inequalities, we prove that the solution vanishes in finite time. This phenomenon is called "quenching"
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Mourougane, Christophe. "Notions de positivité et d'amplitude des fibrés vectoriels : théorèmes d'annulation sur les variétés kahlériennes." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10028.
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L'objet de cette these est l'etude des proprietes de positivite algebriques, analytiques et co-homologiques des fibres vectoriels holomorphes sur les varietes kahleriennes compactes lisses. Dans la premiere partie, nous decrivons les proprietes de positivite algebriques et analytiques des fibres vectoriels obtenus comme images directes par des morphismes lisses de fibres en droites numeriquement effectifs adjoints par le fibre canonique relatif. Dans la deuxieme partie, nous etendons aux varietes kahleriennes compactes le theoreme, du a f. Bogomolov, d'annulation des espaces de p-formes holomorphes a valeurs dans un fibre en droites de dual numeriquement effectif. La troisieme partie, motivee par les travaux de m. Green et r. Lazarsfeld, est consacree aux theoremes d'annulation generique des groupes de cohomologie de fibres vectoriels semi-negatifs. Nous decrivons aussi la structure des lieux exceptionnels de cohomologie
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Gawell, Elin. "Centra of Quiver Algebras." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-106734.
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A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. We describe the center of a partly (anti-)commutative quiveralgebra and state necessary and sufficient conditions for the center to be finitely genteratedas a K-algebra.Examples are provided of partly (anti-)commutative quiver algebras that are Koszul algebras. Necessary and sufficient conditions for finite generation of the Hochschild cohomology ring modulo nilpotent elements for a partly (anti-)commutative Koszul quiver algebra are given.
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Silva, Wagner Ferreira da. "Informação, velocidade da luz e pontos não analíticos." Universidade Federal de Alagoas, 2007. http://repositorio.ufal.br/handle/riufal/994.
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The work begins with a review on the concept of group and phase velocity, and a discussion
about pulses propagation in dispersive media. After that, we are going to study
the Helmholtz equation, followed by Drude-Lorentz s model description of electric susceptibility.
In this study we have analyzed the relations between the real and imaginary part
of the dielectric constant, using Kramers-Kronig relations. Moreover, we have analyzed
the necessary conditions to obtain these relations, and the causality principle. We have
shown physical systems in which is possible to obtain anomalous dispersion. The systems
are population inversion, system with gain-assisted and photonic crystal.
To understand better about some mathematical methods used to study the propagation
of pulses, we have reviewed Fourier, Laplace and Green s methods. We used the
wave equation to show how the methods mentioned above became a problem simpler to
be solved. Finally, we have studied Cauchy-Riemann s conditions and the analyticity of
real and imaginary functions.
We have studied the propagation of Gaussian pulse and a compact support pulse, in
the anomalous dispersion region. We have shown that the Gaussian pulse can propagate
with a bigger group velocity than the speed of light in the vacuum, and these results are
the same when we use the whole expression for the refractive index or not. However, in
the case of the compact support pulse we have seen that is not true. On the other
hand, in the study of the compact support pulse propagation, it was observed that the non-analytical points never exceed the speed of light in the vacuum. Associating
the information to the non-analytical points we have observed the impossibility to send
information faster than light in the vacuum.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
O trabalho inicia com uma revisão sobre o conceito de velocidade de grupo e de fase, e uma breve discussão do que ocorre quando um pulso se propaga num meio dispersivo. Em seguida, fazemos um estudo da equação de onda de Helmholtz, seguido por uma descrição do modelo de Drude-Lorentz para a susceptibilidade elétrica. Durante este estudo exploramos as relações que existem entre a parte real e imaginária da constante dielétrica, através da relação de Kramers-Kronig. Além disso, discutimos o que é necessário na obtenção deste tipo de relação além do princípio de causalidade. Apresentamos os seguintes sistemas físicos nos quais é possível obter regiões com dispersão anômala: sistema com inversão de população, com ganho assistido e cristal fotônico. Com o objetivo de aprofundar o entendimento das ferramentas matemáticas usadas no estudo da propagação de pulsos, revisamos os métodos de Fourier, de Laplace e de Green. Aplicamos estes métodos na equação de onda para mostrar como os mesmos tornam o problema mais simples de ser resolvido. Por fim, estudamos as condições de Cauchy-Riemann e a analiticidade de funções reais e imaginárias. Estudamos a propagação de um pulso Gaussiano e de um pulso com suporte compacto, na região de dispersão anômala. Mostramos que um pulso Gaussiano se propaga com uma velocidade de grupo maior que a velocidade da luz no vácuo, e que o resultado obtido é o mesmo se usarmos somente a parte real do índice de refração ou se usarmos a expressão completa no estudo da propagação. No caso de um pulso com suporte compacto vimos que isto não é verdade. Percebemos ainda que na propagação do pulso com suporte compacto os pontos não analíticos nunca excedem a velocidade da luz no vácuo. Associando a informação a pontos não analíticos mostramos ser impossível enviar informação mais rápida que a luz no vácuo.
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Scipioni, Angel. "Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles." Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10125.
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La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonoreThe necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information
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Kooistra, Remkes. "Real Regulators on Compact Complex Manifolds." Phd thesis, 2010. http://hdl.handle.net/10048/1677.
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This thesis pursues the study of non-algebraic and non-Kahler compact complex manifolds by traditionally algebraic methods involving sheaves, cohomology and K-theory. To that end, Bott-Chern cohomology is developed to complement De Rham and Dolbeault cohomology. The first substantial chapter is devoted to the construction of Bott-Chern cohomology, including products. The next chapter is an investigation of Pic0(X) for non-Kahler complex manifolds. The next chapter uses line bundles represented by classes in this Pic0(X), along with Cartier divisors, to define a group of twisted cycle classes, generalizing a previous algebraic definition. On this group of twisted cycle classes, we use currents to construct a regulator map into Bott-Chern cohomology. Finally, in a chapter of conjectural statements and future directions, we explore the possibility of an alternate regulator using a cone complex of currents. We also conjecturally define a height pairing for certain kinds of compatible twisted cycle classes.Mathematics
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Bagci, Irfan. "Cohomology and support varieties for Lie superalgebras." 2009. http://purl.galileo.usg.edu/uga%5Fetd/bagci%5Firfan%5F200905%5Fphd.
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Thesis (Ph. D.)--University of Georgia, 2009.Directed by Daniel K. Nakano. Includes an article published in International mathematics research notices. For abstract see https://getd.libs.uga.edu/pdfs/bagci%5Firfan%5F200905%5Fphd.pdf. Includes bibliographical references.
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Philip, Eliza. "Function Theory On Non-Compact Riemann Surfaces." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2330.
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The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multi-valued functions. Such multi-valued functions occur because the analytic continuation of a given holomorphic function element along different paths leads in general to different branches of that function. The theory splits in two parts; the compact and the non-compact case. The function theory developed on these cases are quite dissimilar. The main difficulty one encounters in the compact case is the scarcity of global holomorphic functions, which limits one’s study to meromorphic functions. This however is not an issue in non-compact Riemann surfaces, where one enjoys a vast variety of global holomorphic functions. While the function theory of compact Riemann surfaces is centered around the Riemann-Roch theorem, which essentially tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles, the function theory developed on non-compact Riemann surface engages tools for approximation of functions on certain subsets by holomorphic maps on larger domains. The most powerful tool in this regard is the Runge’s approximation theorem. An intriguing application of this is the Gunning-Narasimhan theorem, which says that every connected open Riemann surface has an immersion into the complex plane. The main goal of this project is to prove Runge’s approximation theorem and illustrate its effectiveness in proving the Gunning-Narasimhan theorem. Finally we look at an analogue of Gunning-Narasimhan theorem in the case of a compact Riemann surface.
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Bletz-Siebert, Oliver [Verfasser]. "Homogeneous spaces with the cohomology of sphere products and compact quadrangles / vorgelegt von Oliver Bletz-Siebert." 2002. http://d-nb.info/966590341/34.
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"Compact support wavelet representations for solution of quantum and electromagnetic equations: Eigenvalues and dynamics." Thesis, 2010. http://hdl.handle.net/1911/62118.
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Wavelet-based algorithms are developed for solution of quantum and electromagnetic differential equations. Wavelets offer orthonormal localized bases with built-in multiscale properties for the representation of functions, differential operators, and multiplicative operators. The work described here is part of a series of tools for use in the ultimate goal of general, efficient, accurate and automated wavelet-based algorithms for solution of differential equations.
The most recent work, and the focus here, is the elimination of operator matrices in wavelet bases. For molecular quantum eigenvalue and dynamics calculations in multiple dimensions, it is the coupled potential energy matrices that generally dominate storage requirements. A Coefficient Product Approximation (CPA) for the potential operator and wave function wavelet expansions dispenses with the matrix, reducing storage and coding complexity. New developments are required, however. It is determined that the CPA is most accurate for specific choices of wavelet families, and these are given here. They have relatively low approximation order (number of vanishing wavelet function moments), which would ordinarily be thought to compromise both wavelet reconstruction and differentiation accuracy. Higher-order convolutional coefficient filters are determined that overcome both apparent problems. The result is a practical wavelet method where the effect of applying the Hamiltonian matrix to a coefficient vector can be calculated accurately without constructing the matrix.
The long-familiar Lanczos propagation algorithm, wherein one constructs and diagonalizes a symmetric tridiagonal matrix, uses both eigenvalues and eigenvectors. We show here that time-reversal-invariance for Hermitian Hamiltonians allows a new algorithm that avoids the usual need to keep a number Lanczos vectors around. The resulting Conjugate Symmetric Lanczos (CSL) method, which will apply for wavelets or other choices of basis or grid discretization, is simultaneously low-operation-count and low-storage. A modified CSL algorithm is used for solution of Maxwell's time-domain equations in Hamiltonian form for non-lossy media. The matrix-free algorithm is expected to complement previous work and to decrease both storage and computational overhead. It is expected- that near-field electromagnetic solutions around nanoparticles will benefit from these wavelet-based tools. Such systems are of importance in plasmon-enhanced spectroscopies.
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(10724076), Daniel L. Bath. "Bernstein--Sato Ideals and the Logarithmic Data of a Divisor." Thesis, 2021.
Find full textAbstract:
We study a multivariate version of the Bernstein–Sato polynomial, the so-called Bernstein–Sato ideal, associated to an arbitrary factorization of an analytic germ f - f1···fr. We identify a large class of geometrically characterized germs so that the DX,x[s1,...,sr]-annihilator of fs11···fsrr admits the simplest possible description and, more-over, has a particularly nice associated graded object. As a consequence we are able to verify Budur’s Topological Multivariable Strong Monodromy Conjecture for arbitrary factorizations of tame hyperplane arrangements by showing the zero locus of the associated Bernstein–Sato ideal contains a special hyperplane. By developing ideas of Maisonobe and Narvaez-Macarro, we are able to find many more hyperplanes contained in the zero locus of this Bernstein–Sato ideal. As an example, for reduced, tame hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial contained in [−1,0) are combinatorially determined; for reduced, free hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial are all combinatorially determined. Finally, outside the hyperplane arrangement setting, we prove many results about a certain DX,x-map ∇A that is expected to characterize the roots of the Bernstein–Sato ideal.
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Rippl, Thomas. "Pathwise Uniqueness of the Stochastic Heat Equation with Hölder continuous o diffusion coefficient and colored noise." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F0ED-A.
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