Die abgeschlossenen Erweiterungen der sogenannten geometrischen Operatoren (Spin-Dirac, Gauß-Bonnet und Signatur-Operator) auf Mannigfaltigkeiten mit metrischen Hörnern sind Fredholm-Operatoren und ihr Index wurde von Matthias Lesch, Norbert Peyerimhoff und Jochen Brüning berechnet. Es wurde gezeigt, dass die Einschränkungen dieser drei Operatoren auf eine punktierte Umgebung des singulären Punkts unitär äquivalent zu irregulär singulären Operator-wertigen Differentialoperatoren erster Ordnung sind. Die Lösungsoperatoren der dazugehörigen Differentialgleichungen definierten eine Parametrix, mit deren Hilfe die Fredholmeigenschaft bewiesen wurde. In der vorliegenden Doktorarbeit wird eine Klasse von irregulären singulären Differentialoperatoren erster Ordnung, genannt Horn-Operatoren, eingeführt, die die obigen Beispiele verallgemeinern. Es wird bewiesen, dass ein elliptischer Differentialoperator erster Ordnung, dessen Einschränkung auf eine punktierte Umgebung des singulären Punkts unitär äquivalent zu einem Horn-Operator ist, Fredholm ist, und sein Index wird berechnet. Schließlich wird dieser abstrakte Index-Satz auf geometrische Operatoren auf Mannigfaltigkeiten mit "multiply warped product"-Singularitäten angewendet, welche eine wesentliche Verallgemeinerung der metrischen Hörner darstellen. / The closed extensions of geometric operators (Spin-Dirac, Gauss-Bonnet and Signature operator) on a manifold with metric horns are Fredholm operators, and their indices were computed by Matthias Lesch, Norbert Peyerimhoff and Jochen Brüning. It was shown that the restrictions of all three operators to a punctured neighbourhood of the singular point are unitary equivalent to a class of irregular singular operator-valued differential operators of first order. The solution operators of the corresponding differential equations defined a parametrix which was applied to prove the Fredholm property. In this thesis a class of irregular singular differential operators of first order - called horn operators - is introduced that extends the examples mentioned above. It is proved that an elliptic differential operator of first order whose restriction to the neighbourhood of the singular point is unitary equivalent to a horn operator is Fredholm and its index is computed. Finally, this abstract index theorem is applied to compute the indices of geometric operators on manifolds with multiply warped product singularities that extend the notion of metric horns considerably.

Doctorat en philosophie et lettres / info:eu-repo/semantics/nonPublished

Abstract This report focuses on the creation of a software to calculate handling forces of bonnet and tailgate. The handling force is the force required by a user to open or close a tailgate. It is a bachelor thesis conducted for Karlstad’s university. The work is conducted at CEVT in Gothenburg, the software will be used to improve workflow in early design phases. The resulting software from this project is easy to use and shows good resemblance to the reference values, which is old calculations done by a manufacturer. Comparing to manufacturer calculation the software shows only small deviations in results. The software is deemed to be an asset in the development work at CEVT. The software is also easy to use and have been tested by employees, whom could operate the software easily without instructions. It is based on regular equilibrium equations and the software structure is logical and easy to follow, to make it simple to maintain and develop the software if the need would arise. The finished software calculates single pivot hinges and four bar mechanism-based hinges equipped with gas springs. It also has the possibility to work with tailgate and bonnet simultaneously to keep one project in one file. The work has focused on, creating the software, user interfaces and kinematics/kinetics of different types of hinges, with support from both literature and reports. This led to a software built in Microsoft Excel, which was chosen due to its standard features for graphical display of data. Building the software in Excel also makes it accessible to all employees who wishes to use it. The conclusion is that the software could in extension lead to higher quality on finished products by allowing more tested configurations and continuous changes during the design process. / Sammanfattning Denna rapport behandlar utveckling av mjukvara för att beräkna hanteringskrafter. Hanteringskrafter är de krafter som krävs av användaren för att operera motorhuv och baklucka. Projektet är genomfört som ett examensarbete på Karlstads universitet. Arbetet utförs hos CEVT i Göteborg, där resultatet av arbetet kommer användas för att förbättra designprocessen i tidiga stadier. Den slutgiltiga mjukvaran är enkel att använda och uppvisar resultat som ligger nära referensvärdena, som är gamla beräkningar gjorda av en tillverkare. Endast mindre avvikelser finns mellan beräkningarna. Mjukvaran bedöms vara en tillgång I designarbetet hos CEVT. Mjukvaran är också enkel att använda och har testats av de anställda som kunde använda mjukvaran utan instruktioner. Den är baserad på vanliga jämnviktsekvationer, medan strukturen i programmet är enkel att följa och förstå, detta för att göra det enkelt att underhålla och utveckla om behovet uppstår. Den slutgiltiga mjukvaran beräknar vanliga gångjärn och gångjärn baserade på fyrledsmekanismer utrustade med gasfjädrar. Mjukvaran ger också möjlighet att jobba med både motorhuv och baklucka samtidigt för att kunna hålla ett projekt inom en fil. Arbetets fokus har legat på att, skapa mjukvaran, användargränssnitt och kinematik/kinetik hos olika typer av gångjärn, med stöd inom både litteratur och rapporter. Detta resulterade i en mjukvara byggd i Microsoft Excel, som valdes på grund av dess funktioner för att grafiskt representera data. Att skapa mjukvaran i Excel innebar också att alla på företaget kan använda mjukvaran. Slutsatsen är att mjukvaran skapar en möjlighet att höja kvalitén på färdiga produkter genom att möjliggöra fler testade konfigurationer och kontinuerliga förändringar under designprocessen.

Les trous noirs primordiaux sont une sonde exceptionnelle pour rechercher des effets de nouvelle physique, à l'intersection de la relativité générale, de la mécanique quantique, de la physique des particules et de la cosmologie. Ce mémoire présente quelques pistes d'études relatives à ces objets astrophysiques fascinants. D'abord, autour de leur recherche via l'étude des rayons cosmiques qui seraient émis par évaporation de Hawking. Des liens entre les limites obtenues et les modèles d'inflation sont ensuite proposés afin d'obtenir une borne supérieure très contraignante - et totalement inaccessible aux observables usuelles que sont le fond diffus et les grandes structures - sur la puissance aux petites échelles dans l'Univers primordial. La fin de l'évaporation des trous noirs est etudiée en gravité de corde et leur statut de candidat à la matière noire froide revisité dans le cadre des modèles à brisure d'invariance d'échelle. Enfin, dans le cadre des modèles à basse échelle de Planck (c'est-à-dire présentant de larges dimensions supplémentaires), la formation de trous noirs auprès des collisionneurs est envisagée. Nous montrons que des effets de gravité quantique (couplage de Gauss-Bonnet) pourraient être sondés au LHC. Quelques voies d'investigations futures, liées à la présence d'une constante cosmologique ou au rayonnement cosmique d'énergie extrême sont esquissées.

I detta kandidatarbete undersöker och jämför vi två olika metoder för att approximera gauss- och medelkrökningen hos en yta i rummet som är given som en mängd av punkter. Det är viktigt att försöka få en bra analogi mellan diskret krökning och analytisk krökning då man ofta startar med en mängd punkter i de praktiska fallen, som t ex i tillverkningsindustrin, igenkänning av objekt (inscannade bilder) och datorgrafik. Givet dessa punkter och en bra approximation av gauss- och medelkrökningen kan man få mer information om ytans geometri och beteende. För att kunna förstå dessa begrepp och metoder/algoritmer så behandlas först den bakomliggande teorin och sedan metoderna. Den första metoden är att återge ytan med hjälp av Bézierytor, vilka vi kan utföra geometriska operationer på utan problem och även få fram gauss- och medelkrökningen. Den andra metoden kommer från artikeln ``Discrete Differential-Geometry Operators for Triangulated 2-Manifolds'' av Mark Meyer, Mathieu Desbrun, Peter Schröder och Alan H. Barr. Deras approximationer av krökningarna kräver en triangulering av ytan, vilket de inte ger någon algoritm för. De tittar på ett område runt varje punkt och approximerar krökningarna genom detta område, även Gauss-Bonnets sats används för approximering av gausskrökningen. Mina simuleringar visar att Bézierytornas approximationer av gauss- och medelkrökningar är konvergenta och att alla värden ligger relativt nära varandra. Artikelns algoritm fungerar bra för gauss- och medelkrökning men deras algoritm beror väldigt mycket på trianguleringen vilket gör att man behöver ha krav på den triangulerade ytan, vilket i sig är ett svårt problem att lösa. / In this thesis we analyze and compare two different methods for approximating the Gauss and mean curvature on a surface, which is given as a set of points. It is important to find a method that agrees well with the analytic Gauss and mean curvatures and guarantees robust estimations. There is a great interest in Gauss and mean curvature since these two curvatures give information about the local geometry of the surface around the point at which these curvatures are calculated. The thesis begins with a short overview of differential theory and then the methods are explained and described. The reason for this is to give the reader an understanding of the theory before explaining the methods. The first method is called Bézier surfaces, which interpolates the given points. These surfaces are differentiable which makes it possible to approximate the Gauss and mean curvature, and are therefore very well suited for our problem. The second method comes from the research article ``Discrete Differential-Geometry Operators for Triangulated 2-Manifolds'' by Mark Meyer, Mathieu Desbrun, Peter Schröder and Alan H. Barr. Their algorithm requires a triangulated surface, which itself is a hard problem to solve (at least if one has requirements on the triangulation). Their approximations of the Gauss and mean curvatures use a well chosen area around the point, and the Gauss curvature also makes use of the Gauss-Bonnet theorem. My simulations show that Bézier surfaces approximate both Gauss and mean curvature well, and the approximations seem to converge to the analytic value when the information gets better. The articles algorithm also works well for approximating both curvatures, though this method seems to depend somewhat on the triangulation. This gives some requirements on the triangulation and will therefore be a harder problem to solve. The approximations do not converge when given a triangulation with obtuse triangles, though it shows signs to do so.

I construct anti-de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a (D-1)/(2)-tuplet of complex massless scalar field both perturbativelyand numerically in D=5,7,9,11 dimensions. Due to the choice of scalar fields, these solutions possess just a single helical Killing symmetry. For each choice of the Gauss-Bonnet parameter &alpha;&#8800;&alpha;_cr, the central energy density at the center of the boson star, q_0 completely characterizes the one parameter family of solutions. These solutions obey the first law of thermodynamics, in the case of the numerics, to within 1 part in 10^6. I describe the dependence of the boson star mass, angular momentum and angular velocity on &alpha; and on the dimensionality. For &alpha;<&alpha;_cr and D>5, these quantities exhibit damped oscillations about finite central values and the central energy density tends to infinity. The Kretschmann invariant at the center of the boson star diverges in the limit of diverging central energy. This contrasts the D=5 case, where the Kretschmann invariant diverges at a finite value of the central energy density. Solutions where &alpha;<&alpha;_cr, correspond to negative mass boson stars, and the for all dimensions the boson star mass and angular momentum decrease exponentially as the central energy density tends toward infinity with the Kretschmann invariant diverging only when in the limit the central energy density diverges. I also briefly discuss the difficulties of numerically obtaining single Killing vector hairy black hole solutions and present the explicit boundary conditions for both Einstein gravity and Einstein-Gauss-Bonnet gravity.

Charles Bonnet syndrome (CBS) is defined as complex persistent visual hallucinations in the absence of mental disorder. It is associated with advanced age and poor vision. It is common, with prevalence estimates of up to 63% among older people with significant visual impairment. CBS would not be diagnosed in the presence of dementia, but its relationship to milder cognitive impairment is unclear. The few studies that have examined this are underpowered and provide contradictory results. There are 16 case reports of dementia emerging in people with a diagnosis of CBS. These cases raise the possibility of an association between impaired insight at diagnosis of CBS and the subsequent development of dementia. This thesis reports the findings of a prospective cohort study which describes changes in cognitive functioning over one year in patients with CBS and age-matched controls. Participants were recruited from low vision and glaucoma assessment clinics. A clinical assessment was carried out by an old age psychiatrist, and participants had a detailed assessment of visual functioning. This thesis also describes the findings of the first study to use voxel-based morphometry (VBM) to investigate changes in volume of grey and white matter in CBS. Participants were recruited from the same clinics as the cohort study, and underwent MRI scanning on a 1.5T scanner, to a protocol designed to produce 1mm3 voxels. Twelve participants with CBS and ten controls were followed up. Two people in the CBS group developed dementia, while none did in the control group. The CBS group showed a mean change in the score on the Addenbrooke’s cognitive examination (ACE-R) of -3.7 points, compared to a change of +1.4 in the control group. This difference was not statistically significant. The CBS participants performed worse on the verbal fluency item of the ACE-R, a difference which was statistically significant. The VBM analysis was conducted on 11 CBS participants and 11 controls. The CBS group showed an increase in grey matter volume in the right cerebellar hemisphere. This difference retained significance after family-wise error correction, non-stationary correction, and ANCOVA to control for the effects of possible confounders. As far as the author is aware, these are the most methodologically robust studies to date to have investigated cognition and morphological brain changes in CBS. The findings of the cohort study were inconclusive. However, the two cases of dementia in CBS patients add weight to the suspicion that this is a clinically important outcome in the condition, and the finding of abnormalities in frontal lobe testing in participants with CBS fits with a theoretical model of visual hallucination generation. Moreover, this type of research appears to be acceptable to a frail and visually disabled population, and studies powered to investigate this issue more fully would be feasible. The VBM findings report the presence of underlying structural brain abnormalities in CBS, in a region not usually associated with visual hallucinations. Possible links with Lewy body dementia, and implications for theories of visual hallucinations, are discussed.

This thesis deals with the influence of passive safety features during vehicle collisions with pedestrians. The first part focuses on introducing the basic components of active and passive vehicle safety. The second part deals with construction and usage of modern components of passive safety during vehicle collisions with pedestrians. A comparing situation model of vehicle collisions with pedestrian is introduced in the third part for which a simulation programme has been used. At the close of this part there is a result synthesis of these model situations. The last part deals with the possibility of increasing pedestrian safety.

On étudie différentes notions de courbure riemanniennes: la $p$-courbure, qui interpole entre courbure scalaire et courbure sectionnelle, les courbures de Gauss-Bonnet-Weyl qui constituent une autre interpolation allant de la courbure scalaire <br />jusqu'à l'intégrand de Gauss-Bonnet.<br />Les $(p,q)$-courbures que nous dégageons englobent toutes ces notions. On examine ensuite le terme en courbure de la formule classique de Weitzenböck. On étudie aussi les propriétés de positivité de la $p$-courbure, la seconde courbure de Gauss-Bonnet-Weyl, la courbure d'Einstein et de la courbure isotrope.

In response to LH surge, the selected dominant follicle undergoes a series of complex events viz., meiotic maturation of the oocyte, terminal differentiation of follicular cells, cumulus expansion and follicular rupture leading to ovulation (release of fertilizable oocyte) and formation of corpus luteum. These complex set of events are mediated by dramatic changes in the temporo-spatial transcriptional regulation of a large number of genes in the preovularory follicle. In the present thesis, attempts have been made to delineate the transcriptional changes occurring in the periovulatory follicle in response to gonadotropin surge in monovulatory species (bonnet monkeys and buffalo cows). Further, attempts have also been made to investigate effects of increased circulating IGF-I and glucose on the periovulatory events. Chapter I provides a review of available literature on regulation and factors influencing various aspects of growth and development of ovarian follicles. Chapter II describes initial studies carried out in the bonnet monkeys to examine expression patterns of various genes considered as markers of ovulation and luteinization in granulosa cells of multiple preovulatory-like follicles before and after exposure to luteinizing dose of hCG. Chapter III describes the standardization and validation of an induced ovulation model system in buffalo cows involving determination of the presence of a large follicle by ultrasonography before administering exogenous PGF2αon day 7 of the cycle to induce luteolysis and administration of hCG 36 h post PGF2αto mimic LH surge-like stimulus. Attempts made to characterize the responsiveness of buffalo cows to a range of exogenous doses of GnRH in terms of LH secretion during summer and winter seasons and determination of the exogenous dose of GnRH necessary to elicit a surge-like increase in circulating LH levels during breeding season in buffalo cows are described in Chapter IV. Chapter V describes the global changes in the gene expression pattern in the periovulatory follicle of buffalo cows before and at various time points after the onset of gonadotropin surges. IGF-I is known to regulate the proliferation and survival of follicular cells and play an important role in the selection of dominant follicle however, its role during the periovulatory events remains to be delineated. Chapter VI describes the effects of increased circulating and intrafollicular IGF-I levels on the periovulatory events. An ongoing study to delineate the effects of transient increase in circulating glucose levels on the periovulatory events are described in Appendix I. Thus, this thesis aims at delineating (i) changes in the gene expression patterns regulating periovulatory events and (ii) effects of increased circulating IGF-I and glucose on the periovulatory events.