Heterotic string on the CHL orbifold of K3

We study N = 2 compactifications of heterotic string theory on the CHL orbifold (K3 x T-2)/Z(N) with N = 2, 3, 5, 7. Z(N) acts as an automorphism on K3 together with a shift of 1/N along one of the circles of T-2. These compactifications generalize the example of the heterotic string on K3 x T-2 studied in the context of dualities in string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can be written in terms of the McKay-Thompson series associated with the Z(N) automorphism embedded in the Mathieu group M-24. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of N = 4 string theories.

Heterotic string on the CHL orbifold of K3

We study N = 2 compactifications of heterotic string theory on the CHL orbifold (K3 x T-2)/Z(N) with N = 2, 3, 5, 7. Z(N) acts as an automorphism on K3 together with a shift of 1/N along one of the circles of T-2. These compactifications generalize the example of the heterotic string on K3 x T-2 studied in the context of dualities in string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can be written in terms of the McKay-Thompson series associated with the Z(N) automorphism embedded in the Mathieu group M-24. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of N = 4 string theories.

Special Frobenius Traces in Galois Representations

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues a_p of classical elliptical modular newforms f of weight 2 are never extremal, i.e., a_p is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

Handheld-assisted field data collection for occupational risk assessment.

A computerized handheld procedure is presented in this paper. It is intended as a database complementary tool, to enhance prospective risk analysis in the field of occupational health. The Pendragon forms software (version 3.2) has been used to implement acquisition procedures on Personal Digital Assistants (PDAs) and to transfer data to a computer in an MS-Access format. The data acquisition strategy proposed relies on the risk assessment method practiced at the Institute of Occupational Health Sciences (IST). It involves the use of a systematic hazard list and semi-quantitative risk assessment scales. A set of 7 modular forms has been developed to cover the basic need of field audits. Despite the minor drawbacks observed, the results obtained so far show that handhelds are adequate to support field risk assessment and follow-up activities. Further improvements must still be made in order to increase the tool effectiveness and field adequacy.

Reticulados modulares em espaços euclidianos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Survey Article: Characterizations of the Saito-Kurokawa Lifting

There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Complex Hyperbolic Surfaces of Abelian Type

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

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

Towards a modular robotics standard for AGV design and programming

Across the world there are many bodies currently involved in researching into the design of autonomous guided vehicles (AGVs). One of the greatest problems at present however, is that much of the research work is being conducted in isolated groups, with the resulting AGVs sensor/control/command systems being almost completely nontransferable to other AGV designs. This paper describes a new modular method for robot design which when applied to AGVs overcomes the above problems. The method is explained here with respect to all forms of robotics but the examples have been specifically chosen to reflect typical AGV systems.

Crystallization of Escherichia coli Catabolite Gene Activator Protein with its DNA Binding Site: The use of Modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments ≥28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5′ or 3′ termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (≥28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 Å resolution. Additives such as calcium, n-octyl-β-d-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.

The Ciao clp(FD) library. A modular CLP extension for Prolog

We present a new free library for Constraint Logic Programming over Finite Domains, included with the Ciao Prolog system. The library is entirely written in Prolog, leveraging on Ciao's module system and code transformation capabilities in order to achieve a highly modular design without compromising performance. We describe the interface, implementation, and design rationale of each modular component. The library meets several design goals: a high level of modularity, allowing the individual components to be replaced by different versions; highefficiency, being competitive with other TT> implementations; a glass-box approach, so the user can specify new constraints at different levels; and a Prolog implementation, in order to ease the integration with Ciao's code analysis components. The core is built upon two small libraries which implement integer ranges and closures. On top of that, a finite domain variable datatype is defined, taking care of constraint reexecution depending on range changes. These three libraries form what we call the TT> kernel of the library. This TT> kernel is used in turn to implement several higher-level finite domain constraints, specified using indexicals. Together with a labeling module this layer forms what we name the TT> solver. A final level integrates the CLP (J7©) paradigm with our TT> solver. This is achieved using attributed variables and a compiler from the CLP (J7©) language to the set of constraints provided by the solver. It should be noted that the user of the library is encouraged to work in any of those levels as seen convenient: from writing a new range module to enriching the set of TT> constraints by writing new indexicals.

Construcción modular ligera energéticamente eficiente

Esta tesis trata sobre la construcción modular ligera, dentro del contexto de la eficiencia energética y de cara a los conceptos de nZEB (near Zero Energy Building) y NZEB (Net Zero Energy Building) que se manejan en el ámbito europeo y específicamente dentro del marco regulador de la Directiva 2010/31 UE. En el contexto de la Unión Europea, el sector de la edificación representa el 40% del total del consumo energético del continente. Asumiendo la necesidad de reducir este consumo se han planteado, desde los organismos de dirección europeos, unos objetivos (objetivos 20-20-20) para hacer más eficiente el parque edificatorio. Estos objetivos, que son vinculantes en términos de legislación, comprometen a todos los estados miembros a conseguir la meta de reducción de consumo y emisiones de GEI (Gases de Efecto Invernadero) antes del año 2020. Estos conceptos de construcción modular ligera (CML) y eficiencia energética no suelen estar asociados por el hecho de que este tipo de construcción no suele estar destinada a un uso intensivo y no cuenta con unos cerramientos con niveles de aislamiento de acuerdo a las normativas locales o códigos de edificación de cada país. El objetivo de nZEB o NZEB, e incluso Energy Plus, según sea el caso, necesariamente (y así queda establecido en las normativas), dependerá no sólo de la mejora de los niveles de aislamiento de los edificios, sino también de la implementación de sistemas de generación renovables, independientemente del tipo de sistema constructivo con el que se trabaje e incluso de la tipología edificatoria. Si bien es cierto que los niveles de industrialización de la sociedad tecnológica actual han alcanzado varias de las fases del proceso constructivo - sobre todo en cuanto a elementos compositivos de los edificios- también lo es el hecho de que las cotas de desarrollo conseguidas en el ámbito de la construcción no llegan al nivel de evolución que se puede apreciar en otros campos de las ingenierías como la aeronáutica o la industria del automóvil. Aunque desde finales del siglo pasado existen modelos y proyectos testimoniales de construcción industrializada ligera (CIL) e incluso ya a principios del siglo XX, ejemplos de construcción modular ligera (CML), como la Casa Voisin, la industrialización de la construcción de edificios no ha sido una constante progresiva con un nivel de comercialización equiparable al de la construcción masiva y pesada. Los términos construcción industrializada, construcción prefabricada, construcción modular y construcción ligera, no siempre hacen referencia a lo mismo y no siempre son sinónimos entre sí. Un edificio puede ser prefabricado y no ser modular ni ligero y tal es el caso, por poner un ejemplo, de la construcción con paneles de hormigón prefabricado. Lo que sí es una constante es que en el caso de la construcción modular ligera, la prefabricación y la industrialización, casi siempre vienen implícitas en muchos ejemplos históricos y actuales. Con relación al concepto de eficiencia energética (nZEB o incluso NZEB), el mismo no suele estar ligado a la construcción modular ligera y/o ligera industrializada; más bien se le ve unido a la idea de cerramientos masivos con gran inercia térmica propios de estándares de diseño como el Passivhaus; y aunque comúnmente a la construcción ligera se le asocian otros conceptos que le restan valor (corta vida útil; función y formas limitadas, fuera de todo orden estético; limitación en los niveles de confort, etc.), los avances que se van alcanzando en materia de tecnologías para el aprovechamiento de la energía y sistemas de generación renovables, pueden conseguir revertir estas ideas y unificar el criterio de eficiencia + construcción modular ligera. Prototipos y proyectos académicos– como el concurso Solar Decathlon que se celebra desde el año 2002 promovido por el DOE (Departamento de Energía de los Estados Unidos), y que cuenta con ediciones europeas como las de los años 2010 y 2012, replantean la idea de la construcción industrializada, modular y ligera dentro del contexto de la eficiencia energética, con prototipos de viviendas de ± 60m2, propuestos por las universidades concursantes, y cuyo objetivo es alcanzar y/o desarrollar el concepto de NZEB (Net Zero Energy Building) o edificio de energía cero. Esta opción constructiva no sólo representa durabilidad, seguridad y estética, sino también, rapidez en la fabricación y montaje, además de altas prestaciones energéticas como se ha podido demostrar en las sucesivas ediciones del Solar Decathlon. Este tipo de iniciativas de desarrollo de tecnologías constructivas, no sólo apuntan a la eficiencia energética sino al concepto global de energía neta, Energía plus o cero emisiones de CO2. El nivel de emisiones por la fabricación y puesta en obra de los materiales de construcción depende, en muchos casos, no solo de la propia naturaleza del material, sino también de la cantidad de recursos utilizados para producir una unidad de medida determinada (kg, m3, m2, ml, etc). En este sentido podría utilizarse, en muchos casos, el argumento válido de que a menos peso, y a menos tamaño, menos emisiones globales de gases de efecto invernadero y menos contaminación. Para el trabajo de investigación de esta tesis se han tomado como referencias válidas para estudio, prototipos tanto de CML (Modular 3D) como de CIL (panelizado y elementos 2D), dado que para los fines de análisis de las prestaciones energéticas de los materiales de cerramiento, ambos sistemas son equiparables. Para poder llegar a la conclusión fundamental de este trabajo de tesis doctoral - que consiste en demostrar la viabilidad tecnológica/ industrial que supone la combinación de la eficiencia energética y la construcción modular ligera - se parte del estudio del estado de la técnica ( desde la selección de los materiales y los posibles procesos de industrialización en fábrica, hasta su puesta en obra, funcionamiento y uso, bajo los conceptos de consumo cero, cero emisiones de carbono y plus energético). Además -y con un estado de la técnica que identifica la situación actual- se llevan a cabo pruebas y ensayos con un prototipo a escala natural y células de ensayo, para comprobar el comportamiento de los elementos compositivos de los mismos, frente a unas condicionantes climáticas determinadas. Este tipo de resultados se contrastan con los obtenidos mediante simulaciones informáticas basadas en los mismos parámetros y realizadas en su mayoría mediante métodos simplificados de cálculos, validados por los organismos competentes en materia de eficiencia energética en la edificación en España y de acuerdo a la normativa vigente. ABSTRACT This thesis discusses lightweight modular construction within the context of energy efficiency in nZEB (near Zero Energy Building) and NZEB (Net Zero Energy Building) both used in Europe and, specifically, within the limits of the regulatory framework of the EU Directive 2010/31. In the European Union the building sector represents 40% of the total energy consumption of the continent. Due to the need to reduce this consumption, European decision-making institutions have proposed aims (20-20-20 aims) to render building equipment more efficient. These aims are bound by law and oblige all member States to endeavour to reduce consumption and GEI emissions before the year 2020. Lightweight modular construction concepts and energy efficiency are not generally associated because this type of building is not normally meant for intensive use and does not have closures with insulation levels which fit the local regulations or building codes of each country. The objective of nZEB or NZEB and even Energy Plus, depending on each case, will necessarily be associated (as established in the guidelines) not only with the improvement of insulation levels in buildings, but also with the implementation of renewable systems of generation, independent of the type of building system used and of the building typology. Although it is true that the levels of industrialisation in the technological society today have reached several of the building process phases - particularly in the composite elements of buildings - it is also true that the quotas of development achieved in the area of construction have not reached the evolutionary levelfound in other fields of engineering, such as aeronautics or the automobile industry. Although there have been models and testimonial projects of lightweight industrialised building since the end of last century, even going back as far as the beginning of the XX century with examples of lightweight modular construction such as the Voisin House, industrialisation in the building industry has not been constant nor is its comercialisation comparable to massive and heavy construction. The terms industrialised building, prefabricated building, modular building and lightweight building, do not always refer to the same thing and they are not always synonymous. A building can be prefabricated yet not be modular or lightweight. To give an example, this is the case of building with prefabricated concrete panels. What is constant is that, in the case of lightweight modular construction, prefabrication and industrialisation are almost always implicit in many historical and contemporary examples. Energy efficiency (nZEB or even NZEB) is not normally linked to lightweight modular construction and/or industrialised lightweight; rather, it is united to the idea of massive closureswith high thermal inertia typical of design standards such as the Passive House; and although other concepts that subtract value from it are generally associated with lightweight building (short useful life, limited forms and function, inappropriate toany aesthetic pattern; limitation in comfort levels, etc.), the advances being achieved in technology for benefitting from energy and renewable systems of generation may well reverse these ideas and unify the criteria of efficiency + lightweight modular construction. Academic prototypes and projects - such as the Solar Decathlon competition organised by the US Department of Energy and celebrated since 2002, with its corresponding European events such as those held in 2010 and 2012, place a different slant on the idea of industrialised, modular and lightweight building within the context of energy efficiency, with prototypes of homes measuring approximately 60m2, proposed by university competitors, whose aim is to reach and/or develop the NZEB concept, or the zero energy building. This building option does not only signify durability, security and aesthetics, but also fast manufacture and assembly. It also has high energy benefits, as has been demonstrated in successive events of the Solar Decathlon. This type of initiative for the development of building technologies, does not only aim at energy efficiency, but also at the global concept of net energy, Energy Plus and zero CO2 emissions. The level of emissions in the manufacture and introduction of building materials in many cases depends not only on the inherent nature of the material, but also on the quantity of resources used to produce a specific unit of measurement (kg, m3, m2, ml, etc.). Thus in many cases itcould be validly arguedthat with less weight and smaller size, there will be fewer global emissions of greenhouse effect gases and less contamination. For the research carried out in this thesis prototypes such as the CML (3D Module) and CIL (panelled and elements) have been used as valid study references, becauseboth systems are comparablefor the purpose of analysing the energy benefits of closure materials. So as to reach a basic conclusion in this doctoral thesis - that sets out to demonstrate the technological/industrial viability of the combination of energy efficiency and lightweight modular construction - the departure point is the study of the state of the technique (from the selection of materials and the possible processes of industrialisation in manufacture, to their use on site, functioning and use, respecting the concepts of zero consumption, zero emissions of carbon and Energy Plus). Moreover, with the state of the technique identifying the current situation, tests and practices have been carried out with a natural scale prototype and test cells so as to verify the behaviour of the composite elements of these in certain climatic conditions. These types of result are contrasted with those obtained through computer simulation based on the same parameters and done, principally, using simplified methods of calculation, validated by institutions competent in energy efficiency in Spanish building and in line with the rules in force.