Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Explicit methods for Hilbert modular forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Modularity of the Consani-Scholten quintic

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over Q, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livn´e method to induced four-dimensional Galois representations over Q. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author.

Accurate ab initio potential energy surfaces for the (3)A '' and (3)A ' electronic states of the O(P-3) plus HBr system

In this work, we report the construction of potential energy surfaces for the (3)A '' and (3)A' states of the system O(P-3) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O(P-3) + HBr -> OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A '' electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A' surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A '' and 4.16 kcal/mol for the (3)A' state. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705428]

Teoremas de tipo Hilbert e Liebmann para superfícies em S² x R e H² x R

Neste trabalho será demonstrada uma versão dos teoremas de Hilbert Liebmann para superfícies em S² x R e H² x R, que são teoremas de existência e unicidade de superfícies completas com curvatura Gaussiana constante nesses ambientes. Como parte da demonstração, a saber a existência, será apresentada uma classificação das superfícies de revolução completas com curvatura Gaussiana constante em torno de um eixo qualquer, em S² x R e em torno de um eixo lorentziano, em H² x R.

Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

An analytical investigation into shear wall and slab interconnections between reinforced concrete modules for high -rise buildings utilising modular construction under extreme seismic and wind loading

This research investigates a new structural system utilising modular construction. Five-sided boxes are cast on-site and stacked together to form a building. An analytical model was created of a typical building in each of two different analysis programs utilising the finite element method (Robot Millennium and ETABS). The pros and cons of both Robot Millennium and ETABS are listed at several key stages in the development of an analytical model utilising this structural system. Robot Millennium was initially utilised but created an analytical model too large to be successfully run. The computation requirements were too large for conventional computers. Therefore Robot Millennium was abandoned in favour of ETABS, whose more simplistic algorithms and assumptions permitted running this large computation model. Tips are provided as well as pitfalls signalled throughout the process of modelling such complex buildings of this type. ^ The building under high seismic loading required a new horizontal shear mechanism. This dissertation has proposed to create a secondary floor that ties to the modular box through the use of gunwales, and roughened surfaces with epoxy coatings. In addition, vertical connections necessitated a new type of shear wall. These shear walls consisted of waffled external walls tied through both reinforcement and a secondary concrete pour. ^ This structural system has generated a new building which was found to be very rigid compared to a conventional structure. The proposed modular building exhibited a period of 1.27 seconds, which is about one-fifth of a conventional building. The maximum lateral drift occurs under seismic loading with a magnitude of 6.14 inches which is one-quarter of a conventional building's drift. The deflected shape and pattern of the interstorey drifts are consistent with those of a coupled shear wall building. In conclusion, the computer analysis indicate that this new structure exceeds current code requirements for both hurricane winds and high seismic loads, and concomitantly provides a shortened construction time with reduced funding. ^

A model for the modular evolution of rna addressing open questions on the origin of life

A main unsolved problem in the RNA world scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers generated by random polymerization of ribonucleotides (Joyce and Orgel 2006). Current estimates establish a minimum size about 165 nt long for such a ribozyme (Johnston et al. 2001), a length three to four times that of the longest RNA oligomers obtained by random polymerization on clay mineral surfaces (Huang and Ferris 2003, 2006). To overcome this gap, we have developed a stepwise model of ligation-based, modular evolution of RNA (Briones et al. 2009) whose main conceptual steps are summarized in Figure 1. This scenario has two main advantages with respect to previous hypotheses put forward for the origin of the RNA world: i) short RNA....

Fibronectin/phosphorylcholine coatings on fluorocarboned surfaces: a study upon adsorption and grafting processes

Depuis ces dernières décennies, le domaine des biomatériaux a connu un essor considérable, évoluant de simples prothèses aux dispositifs les plus complexes pouvant détenir une bioactivité spécifique. Outre, le progrès en science des matériaux et une meilleure compréhension des systèmes biologiques a offert la possibilité de créer des matériaux synthétiques pouvant moduler et stimuler une réponse biologique déterminée, tout en améliorant considérablement la performance clinique des biomatériaux. En ce qui concerne les dispositifs cardiovasculaires, divers recouvrements ont été développés et étudiés dans le but de modifier les propriétés de surface et d’améliorer l’efficacité clinique des tuteurs. En effet, lorsqu’un dispositif médical est implanté dans le corps humain, son succès clinique est fortement influencé par les premières interactions que sa surface établit avec les tissus et les fluides biologiques environnants. Le recouvrement à la surface de biomatériaux par diverses molécules ayant des propriétés complémentaires constitue une approche intéressante pour atteindre différentes cibles biologiques et orienter la réponse de l’hôte. De ce fait, l’élucidation de l’interaction entre les différentes molécules composant les recouvrements est pertinente pour prédire la conservation de leurs propriétés biologiques spécifiques. Dans ce travail, des recouvrements pour des applications cardiovasculaires ont été créés, composés de deux molécules ayant des propriétés biologiques complémentaires : la fibronectine (FN) afin de promouvoir l’endothélialisation et la phosphorylcholine (PRC) pour favoriser l’hémocompatibilité. Des techniques d’adsorption et de greffage ont été appliquées pour créer différents recouvrements de ces deux biomolécules sur un polymère fluorocarboné déposé par traitement plasma sur un substrat en acier inoxydable. Dans un premier temps, des films de polytétrafluoroéthylène (PTFE) ont été utilisés en tant que surface modèle afin d’explorer l’interaction de la PRC et de la FN avec les surfaces fluorocarbonées ainsi qu’avec des cellules endothéliales et du sang. La stabilité des recouvrements de FN sur l’acier inoxydable a été étudiée par déformation, mais également par des essais statiques et dynamiques sous-flux. Les recouvrements ont été caractérisés par Spectroscopie Photoéléctronique par Rayons X, immunomarquage, angle de contact, Microscopie Électronique de Balayage, Microscopie de Force Atomique et Spectrométrie de Masse à Ionisation Secondaire à Temps de Vol (imagerie et profilage en profondeur). Des tests d’hémocompatibilité ont été effectués et l’interaction des cellules endothéliales avec les recouvrements a également été évaluée. La FN greffée a présenté des recouvrements plus denses et homogènes alors que la PRC quant à elle, a montré une meilleure homogénéité lorsqu’elle était adsorbée. La caractérisation de la surface des échantillons contenant FN/PRC a été corrélée aux propriétés biologiques et les recouvrements pour lesquels la FN a été greffée suivie de l’adsorption de la PRC ont présenté les meilleurs résultats pour des applications cardiovasculaires : la promotion de l’endothélialisation et des propriétés d’hémocompatibilité. Concernant les tests de stabilité, les recouvrements de FN greffée ont présenté une plus grande stabilité et densité que dans le cas de l’adsorption. En effet, la pertinence de présenter des investigations des essais sous-flux versus des essais statiques ainsi que la comparaison des différentes stratégies pour créer des recouvrements a été mis en évidence. D’autres expériences sont nécessaires pour étudier la stabilité des recouvrements de PRC et de mieux prédire son interaction avec des tissus in vivo.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Elementary properties of Modular curves and Modular forms

Lo scopo di questa tesi è introdurre in breve le prime proprietà delle curve modulari e delle forme modulari, per poi mostrarne alcune applicazioni archetipiche. Per farlo, dopo aver richiamato alcune nozioni utili nel primo capitolo, sviluppiamo, nel secondo capitolo, la teoria di base delle curve modulari compatte come superfici di Riemann, calcolandone il genere nel caso dei sottogruppi principali di congruenza. Dunque, nel terzo capitolo, dopo un estesa trattazione dell'esempio delle forme modulari rispetto al gruppo modulare, viene calcolata la dimensione degli spazi delle forme intere e delle forme cuspidali rispetto a un sottogruppo di indice finito del gruppo modulare. Questo capitolo si conclude con tre esempi di applicazione della teoria esposta, tra i quali spiccano la dimostrazione del Grande Teorema di Picard e del Teorema dei quattro quadrati di Jacobi.

Electronic And Structural Study Of Pt-modified Au Vicinal Surfaces: A Model System For Pt-au Catalysts.

Two single crystalline surfaces of Au vicinal to the (111) plane were modified with Pt and studied using scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) in ultra-high vacuum environment. The vicinal surfaces studied are Au(332) and Au(887) and different Pt coverage (θPt) were deposited on each surface. From STM images we determine that Pt deposits on both surfaces as nanoislands with heights ranging from 1 ML to 3 ML depending on θPt. On both surfaces the early growth of Pt ad-islands occurs at the lower part of the step edge, with Pt ad-atoms being incorporated into the steps in some cases. XPS results indicate that partial alloying of Pt occurs at the interface at room temperature and at all coverage, as suggested by the negative chemical shift of Pt 4f core line, indicating an upward shift of the d-band center of the alloyed Pt. Also, the existence of a segregated Pt phase especially at higher coverage is detected by XPS. Sample annealing indicates that the temperature rise promotes a further incorporation of Pt atoms into the Au substrate as supported by STM and XPS results. Additionally, the catalytic activity of different PtAu systems reported in the literature for some electrochemical reactions is discussed considering our findings.

Analysis Of The Fluorescence Of Body Fluids On Different Surfaces And Times.

The use of screening techniques, such as an alternative light source (ALS), is important for finding biological evidence at a crime scene. The objective of this study was to evaluate whether biological fluid (blood, semen, saliva, and urine) deposited on different surfaces changes as a function of the age of the sample. Stains were illuminated with a Megamaxx™ ALS System and photographed with a Canon EOS Utility™ camera. Adobe Photoshop™ was utilized to prepare photographs for analysis, and then ImageJ™ was used to record the brightness values of pixels in the images. Data were submitted to analysis of variance using a generalized linear mixed model with two fixed effects (surface and fluid). Time was treated as a random effect (through repeated measures) with a first-order autoregressive covariance structure. Means of significant effects were compared by the Tukey test. The fluorescence of the analyzed biological material varied depending on the age of the sample. Fluorescence was lower when the samples were moist. Fluorescence remained constant when the sample was dry, up to the maximum period analyzed (60 days), independent of the substrate on which the fluid was deposited, showing the novelty of this study. Therefore, the forensic expert can detect biological fluids at the crime scene using an ALS even several days after a crime has occurred.