Cette thèse est constituée de deux parties complètement indépendantes.Dans une première partie, nous montrons que la paire de Fourier-Mukai (X,Y) issue de la correspondance double miroir Pfaffienne-Grassmannienne vérifie l'identité ([X]-[Y])L^6=0 dans l'anneau de Grothendieck, où L est la classe de la droite affine. Ce résultat est un raffinement d'un théorème de Borisov par la suppression d'un facteur, qui montre que la classe de la droite affine est un diviseur de zéro dans l'anneau de Grothendieck, et fournit par ailleurs un premier exemple intéressant de variétés D-équivalentes qui sont L-équivalentes. D'autres exemples ont par la suite été explicités par d'autres auteurs.Dans une seconde partie, nous nous intéressons au comportement d'invariants de théorie de Hodge par convolution intermédiaire, à la suite des travaux de Dettweiler et Sabbah. Le principal résultat concerne le comportement des données numériques locales de Hodge cycles proches à l'infini par convolution intermédiaire additive par un module de Kummer. Nous donnons également des formules pour les invariants locaux h^p et globaux delta^p sans faire l'hypothèse de monodromie scalaire à l'infini. De plus, à l'aide d'une relation de Katz reliant les convolutions additives et multiplicatives, nous explicitons le comportement des invariants de Hodge par convolution intermédiaire multiplicative. Enfin, le théorème principal permet de redémontrer un résultat de Fedorov sur les invariants de Hodge d'équations hypergéométriques. / This thesis consists of two independent parts.In a first part, we show that the Fourier-Mukai pair (X,Y) constructed from Pfaffian-Grassmannian double-mirror correspondence verifies the formula ([X]-[Y]) L^6=0 in the Grothendieck ring, where L is the class of affine line. This result is an improvement of a theorem of Borisov by removing a factor, which shows that the class of affine line is a zero divisor in the Grothendieck ring, and gives moreover a first interesting example of D-equivalent varieties which are L-equivalent. Other examples have later been made explicit by other authors.In a second part, we are interested in the behaviour of invariants in Hodge theory by middle convolution, following research of Dettweiler and Sabbah. The main result concerns the behaviour of the nearby cycle local Hodge numerical data in infinity by middle additive convolution by a Kummer module. We also give expressions for local invariant h^p and global delta^p without making the hypothesis of scalar monodromy in infinity. Besides, with a relation due to Katz linking up additive and multiplicative convolutions, we explain the behaviour of Hodge invariants by middle multiplicative convolution. Finally, the main theorem gives a new proof of a result of Fedorov on Hodge invariants of hypergeometric equations.

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Positive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative kernels in the setting of Hilbert C*-modules and Hilbert W*-modules. We prove an Arveson-type extension theorem for completely positive noncommutative kernels, and we show that a uniformly bounded noncommutative kernel can be decomposed into a linear combination of completely positive noncommutative kernels. / Ph. D.

I denna rapport kommer en processen av hur en glasfiberprodukt kan designas med utgångspunkt av en likvärdig produkt gjord i stål genomföras. Arbetet är gjort från uppdrag utav Roxtec international AB och handlar om designarbetet för en glasfiberram.Arbetet har gjorts med samarbete med Roxtec och utgår ifrån deras idéer om att designa en ny produkt för att hjälpa dem att få in sin produkt i fler marknader. I detta fall handlar det om att ha en glasfiberram gjord med långa fibrer för att kunna installera Roxtecs produkter i glasfiberskepp och båtar utan att bryta vissa certifikationer. Ramen används för att hålla tätningsmoduler på plats. Dessa tätningsmoduler pressas ihop vilket ger ett stort tryck på ramen.En stor del av arbetet handlar också om att ta reda på vilka olika tillverkningsmetoder som finns för glasfiber och hur de funkar med de koncepten som slutligen tas fram.I de första delarna av rapporten finns bakgrundsinformation om Roxtec och sedan information om de olika tillverkningsmetoderna som finns. Sedan går det vidare med information om de olika metoderna som används för att ta fram resultatet. Efter det fortsätter rapporten genom att visa ett antal koncept som sedan dimensioneras mot kraven som sätts på produkten.I den sista delen av rapporten ges sedan en rekommendation utifrån resultaten till Roxtec om vilken tillverkningsmetod som är lämplig och även en slutgiltig design på en glasfiberram. / In this report, a process of how a fiberglass product can be designed on the basis of an equivalent product made of steel be performed. The work is done through an assignment from Roxtec International AB and is about the design work for a fiberglass frame.The work has been done with cooperation with Roxtec and assumes their ideas about designing a new product in order to help them to get their product into more markets. In this case it is about a fiberglass frame made with long fibers in order to install Roxtec's products in fiberglass ships and boats without breaking certain certifications. The frame is used to hold the sealing modules in place. The sealing modules are then compressed which puts a heavy pressure on the frame.A large part of the work is also about finding out what different manufacturing methods there are for fiberglass and how they work with the concepts that will be developed.The first parts of the report provides background information about Roxtec and then information on the different manufacturing methods available. Then it provides information on the various methods used to produce the result. The report continues by displaying a number of concepts which are then designed to the requirements set on the product.In the last part of the report is a recommendation is given based on the results to Roxtec about which manufacturing method is appropriate and also a final design on a fiberglass frame.

Dans ce mémoire, on commence par introduire le radical de la catégorie mod A pour une algèbre donnée A de dimension finie sur un corps algébriquement clos, avant d'en définir la puissance annulatrice dans le cas où A est de représentation finie. On calcule ensuite cette puissance annulatrice en fonction du nombre de cordes dans le carquois ordinaire Q_A, dans le cas où A est une algèbre inclinée itérée de type A.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This thesis deals with a function eld analog of the André-Oort conjecture. The (classical) André-Oort conjecture concerns the distribution of special points on Shimura varieties. In our case we consider the André-Oort conjecture for special points in the product of Drinfeld modular varieties. We in particular manage to prove the André- Oort conjecture for subvarieties in a product of two Drinfeld modular surfaces under a characteristic assumption. / AFRIKAANSE OPSOMMING: Hierdie tesis handel van 'n funksieliggaam analoog van die André-Oort Vermoeding. Die (Klassieke) André-Oort Vermoeding het betrekking tot die verspreiding van spesiale punte op Shimura varietiete. Ons geval beskou ons die André-Oort Vermoeding vir spesiale punte op die produk Drinfeldse modulvarietiete. In die besonders, bewys ons die André-Oort Vermoeding vir ondervarieteite van 'n produk van twee Drinfeldse modulvarietiete, onderhewig aan 'n karakteristiek-aanname.

For a stress-sensitive or stress-dependent reservoir, the interactions between its seepage field and in situ stress field are complex and affect hydrocarbon recovery. A coupled geomechanics and fluid-flow model can capture these relations between the fluid and solid, thereby presenting more precise history matchings and predictions for better well planning and reservoir management decisions. A traditional reservoir simulator cannot adequately or fully represent the ongoing coupled fluid-solid interactions during the production because of using the simplified update-formulation for porosity and the static absolute permeability during simulations. Many researchers have studied multiphase fluid-flow models coupled with geomechanics models during the past fifteen years. The purpose of this research is to develop a coupled geomechanics and compositional model and apply it to problems in the oil recovery processes. An equation of state compositional simulator called the General Purpose Adaptive Simulator (GPAS) is developed at The University of Texas at Austin and uses finite difference / finite control volume methods for the solution of its governing partial differential equations (PDEs). GPAS was coupled with a geomechanics model developed in this research, which uses a finite element method for discretization of the associated PDEs. Both the iteratively coupled solution procedure and the fully coupled solution procedure were implemented to couple the geomechanics and reservoir simulation modules in this work. Parallelization, testing, and verification for the coupled model were performed on parallel clusters of high-performance workstations. MPI was used for the data exchange in the iteratively coupled procedure. Different constitutive models were coded into GPAS to describe complicated behaviors of linear or nonlinear deformation in the geomechanics model. In addition, the geomechanics module was coupled with the dual porosity model in GPAS to simulate naturally fractured reservoirs. The developed coupled reservoir and geomechanics simulator was verified using analytical solutions. Various reservoir simulation case studies were carried out using the coupled geomechanics and GPAS modules. / text

<p>During papermaking, the internal structure of the fibrenetwork constituting the paper is to a dominating extentdetermined in the forming zone of the paper machine. Thisthesis is aimed at studying the pressure distribution in bladeforming sections, which is commonly considered to be a keyquantity of the process.</p><p>Previous work has provided insight into the physics ofdifferent devices employed in blade forming. However, there hasbeen a lack of models enabling studies of the effects of theinteraction between different components on the pressuredistribution. In the thesis, a model is presented for a genericblade forming section consisting of three blades. The positionsof two of the blades are fix, and in between them is located asuction box. The third blade is applied by a prescribed forceto the opposing wire, in a position facing the suction box. Themodel admits the study of the interaction between the pulsesfrom the different blades in the blade/counterbladeconfiguration, and between the pulses and one-sidedsuction.</p><p>The wires are modelled as tensioned and perfectly flexibleEuler-Bernoulli beams of negligible mass. The suspension istreated like an inviscid fluid. Consideration is taken to theinfluence of fibre deposition on the permeability of thefabrics. By assuming the ratio between the length scales in thethickness direction and the machine direction to be small, aquasi one-dimensional model is obtained.</p><p>For maximum flexibility, the model domain is divided intomodules. Each module is solved individually using a finitedifference based discretisation. The solutions for thedifferent modules are matched with each other iteratively.</p><p>A comparison with published results for a single bladeindicates that the model can be used to obtain qualitativelycorrect predictions of the pressure distribution. New resultsinclude a series of calculations showing the non-trivialinteraction between the pressure pulses when the blades arepositioned successively closer together, the effects of suctionon the pressure pulse generated by a blade applied to theopposing wire, and how blades of modest curvature do notnecessarily stay in contact with the fabric along their fullwidth and the implication of this on the pressure gradient.</p><p><b>Descriptors:</b>fluid mechanics, blade forming, pressuredistribution, suction, interaction, permeable fabric,modules</p>

On étudie la cosmologie induite par un gaz parfait de supercordes à température finie. Les effets thermaux et quantiques du gaz de cordes génèrent un potentiel effectif au niveau d'une boucle. A certains points dans l'espace de modules où les masses des états génériquement massifs s'annulent, le potentiel effectif atteint des minima locaux. Les modules qui y sont attirés prennent des masses qui diminuent avec le temps, ce qui permet aux oscillations cohérentes des modules d'être diluées avant la nucléosynthèse. Ainsi le modèle ne rencontre pas le problème des modules cosmologiques. En particulier, on étudie la stabilisation des modules pour la cosmologie induite par i) un gaz de cordes hétérotiques maximalement supersymétriques, ii) un gaz de cordes de type II compactifiées sur un espace de Calabi-Yau de dimension complexe 3. Dans le 1er cas, les minima locaux du potentiel effectif apparaissent aux points de symétries de jauge étendues. Ceux-ci stabilisent tous les modules sauf le dilaton. Dans le 2ème cas, les minima locaux du potentiel effectif sont atteints où des 2- ou 3-sphères dans l'espace de Calabi-Yau s'évanouissent, produisant une transition conifold ou une extension du groupe non Abelien de jauge. Les états non massifs supplémentaires sont engendrés par des D-branes s'enroulant sur les sphères qui s'évanouissent et les modules stabilisés sont ceux qui contrôlent les volumes de ces sphères. Pour les deux cas, on étudie aussi respectivement les théories duales de type I maximalement supersymétrique et hétérotique compactifiée sur K3xT2. On trouve que les modules duaux sont stabilisés par des effets non perturbatifs impliqués par les dualités concernées.

On étudie dans cette thèse les espaces de modules de fibrés orthogonaux sur une courbe algébrique lisse.<br />On montre dans un premier temps que le morphisme d'oubli associant à un fibré orthogonal le fibré vectoriel sous-jacent est une immersion fermée : ce résultat repose sur un calcul d'invariants sur les espaces de représentations de certains carquois.<br />On présente ensuite, pour les fibrés orthogonaux de rang 3 et 4, des résultats plus concrets sur la géométrie de ces espaces, en accordant une attention particulière à l'application thêta.