Remarks on Lipschitz domains in Carnot groups

In this Note we present the basic features of the theory of Lipschitz maps within Carnot groups as it is developed in [8], and we prove that intrinsic Lipschitz domains in Carnot groups are uniform domains.

Does upward social mobility increase life satisfaction? A longitudinal analysis using British and Swiss panel data

A main assumption of social production function theory is that status is a major determinant of subjective well-being (SWB). From the perspective of the dissociative hypothesis, however, upward social mobility may be linked to identity problems, distress, and reduced levels of SWB because upwardly mobile people lose their ties to their class of origin. In this paper, we examine whether or not one of these arguments holds. We employ the United Kingdom and Switzerland as case studies because both are linked to distinct notions regarding social inequality and upward mobility. Longitudinal multilevel analyses based on panel data (UK: BHPS, Switzerland: SHP) allow us to reconstruct individual trajectories of life satisfaction (as a cognitive component of SWB) along with events of intragenerational and intergenerational upward mobility—taking into account previous levels of life satisfaction, dynamic class membership, and well-studied determinants of SWB. Our results show some evidence for effects of social class and social mobility on well-being in the UK sample, while there are no such effects in the Swiss sample. The UK findings support the idea of dissociative effects in terms of a negative effect of intergenerational upward mobility on SWB.

Modelos determinístico y probabilístico para la estimación de la carga de nitratos en una cuenca rural

En este trabajo se desarrolló un modelo probabilístico que utiliza la teoría de la función de densidad de probabilidades derivada para estimar la carga media anual de nitratos transportada por el escurrimiento superficial, utilizando una relación funcional entre el escurrimiento y la carga de nitratos. El modelo determinístico hidrológico y de calidad de agua denominado Simulator for Water Resources in Rural Basins - Water Quality (SWRRB-WQ) fue utilizado para estimar la carga de nitratos en el escurrimiento superficial. Este modelo emplea como variable de entrada la precipitación diaria observada en la Estación del Aeropuerto de Olavarría durante el período 1988 a 2002. Para la calibración del modelo se aplicó una nueva metodología que estima la incertidumbre en los valores observados. Ambos modelos probabilístico y determinístico se aplican en una subcuenca rural del arroyo Tapalqué (provincia de Buenos Aires, Argentina) y finalmente se comparan los valores de la carga de nitratos estimados con los dos modelos con las observaciones realizadas en la sección del arroyo motivo de este estudio. Los resultados muestran que la carga media de nitratos obtenida con el modelo probabilístico es del mismo orden de magnitud que los valores medios observados y estimados con el modelo hidrológico y de calidad de agua SWRRB-WQ.

Medidas autosemejantes en el plano, momentos y matrices de Hessenberg

La tesis MEDIDAS AUTOSEMEJANTES EN EL PLANO, MOMENTOS Y MATRICES DE HESSENBERG se enmarca entre las áreas de la teoría geométrica de la medida, la teoría de polinomios ortogonales y la teoría de operadores. La memoria aborda el estudio de medidas con soporte acotado en el plano complejo vistas con la óptica de las matrices infinitas de momentos y de Hessenberg asociadas a estas medidas que en la teoría de los polinomios ortogonales las representan. En particular se centra en el estudio de las medidas autosemejantes que son las medidas de equilibrio definidas por un sistema de funciones iteradas (SFI). Los conjuntos autosemejantes son conjuntos que tienen la propiedad geométrica de descomponerse en unión de piezas semejantes al conjunto total. Estas piezas pueden solaparse o no, cuando el solapamiento es pequeño la teoría de Hutchinson [Hut81] funciona bien, pero cuando no existen restricciones falla. El problema del solapamiento consiste en controlar la medida de este solapamiento. Un ejemplo de la complejidad de este problema se plantea con las convoluciones infinitas de distribuciones de Bernoulli, que han resultado ser un ejemplo de medidas autosemejantes en el caso real. En 1935 Jessen y A. Wintner [JW35] ya se planteaba este problema, lejos de ser sencillo ha sido estudiado durante más de setenta y cinco años y siguen sin resolverse las principales cuestiones planteadas ya por A. Garsia [Gar62] en 1962. El interés que ha despertado este problema así como la complejidad del mismo está demostrado por las numerosas publicaciones que abordan cuestiones relacionadas con este problema ver por ejemplo [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05],[JKS07] [JKS11]. En el primer capítulo comenzamos introduciendo con detalle las medidas autosemejante en el plano complejo y los sistemas de funciones iteradas, así como los conceptos de la teoría de la medida necesarios para describirlos. A continuación se introducen las herramientas necesarias de teoría de polinomios ortogonales, matrices infinitas y operadores que se van a usar. En el segundo y tercer capítulo trasladamos las propiedades geométricas de las medidas autosemejantes a las matrices de momentos y de Hessenberg, respectivamente. A partir de estos resultados se describen algoritmos para calcular estas matrices a partir del SFI correspondiente. Concretamente, se obtienen fórmulas explícitas y algoritmos de aproximación para los momentos y matrices de momentos de medidas fractales, a partir de un teorema del punto fijo para las matrices. Además utilizando técnicas de la teoría de operadores, se han extendido al plano complejo los resultados que G. Mantica [Ma00, Ma96] obtenía en el caso real. Este resultado es la base para definir un algoritmo estable de aproximación de la matriz de Hessenberg asociada a una medida fractal u obtener secciones finitas exactas de matrices Hessenberg asociadas a una suma de medidas. En el último capítulo, se consideran medidas, μ, más generales y se estudia el comportamiento asintótico de los autovalores de una matriz hermitiana de momentos y su impacto en las propiedades de la medida asociada. En el resultado central se demuestra que si los polinomios asociados son densos en L2(μ) entonces necesariamente el autovalor mínimo de las secciones finitas de la matriz de momentos de la medida tiende a cero. ABSTRACT The Thesis work “Self-similar Measures on the Plane, Moments and Hessenberg Matrices” is framed among the geometric measure theory, orthogonal polynomials and operator theory. The work studies measures with compact support on the complex plane from the point of view of the associated infinite moments and Hessenberg matrices representing them in the theory of orthogonal polynomials. More precisely, it concentrates on the study of the self-similar measures that are equilibrium measures in a iterated functions system. Self-similar sets have the geometric property of being decomposable in a union of similar pieces to the complete set. These pieces can overlap. If the overlapping is small, Hutchinson’s theory [Hut81] works well, however, when it has no restrictions, the theory does not hold. The overlapping problem consists in controlling the measure of the overlap. The complexity of this problem is exemplified in the infinite convolutions of Bernoulli’s distributions, that are an example of self-similar measures in the real case. As early as 1935 [JW35], Jessen and Wintner posed this problem, that far from being simple, has been studied during more than 75 years. The main cuestiones posed by Garsia in 1962 [Gar62] remain unsolved. The interest in this problem, together with its complexity, is demonstrated by the number of publications that over the years have dealt with it. See, for example, [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05], [JKS07] [JKS11]. In the first chapter, we will start with a detailed introduction to the self-similar measurements in the complex plane and to the iterated functions systems, also including the concepts of measure theory needed to describe them. Next, we introduce the necessary tools from orthogonal polynomials, infinite matrices and operators. In the second and third chapter we will translate the geometric properties of selfsimilar measures to the moments and Hessenberg matrices. From these results, we will describe algorithms to calculate these matrices from the corresponding iterated functions systems. To be precise, we obtain explicit formulas and approximation algorithms for the moments and moment matrices of fractal measures from a new fixed point theorem for matrices. Moreover, using techniques from operator theory, we extend to the complex plane the real case results obtained by Mantica [Ma00, Ma96]. This result is the base to define a stable algorithm that approximates the Hessenberg matrix associated to a fractal measure and obtains exact finite sections of Hessenberg matrices associated to a sum of measurements. In the last chapter, we consider more general measures, μ, and study the asymptotic behaviour of the eigenvalues of a hermitian matrix of moments, together with its impact on the properties of the associated measure. In the main result we demonstrate that, if the associated polynomials are dense in L2(μ), then necessarily follows that the minimum eigenvalue of the finite sections of the moments matrix goes to zero.

Three-dimensional modeling of and ligand docking to vitamin D receptor ligand binding domain

The ligand binding domain of the human vitamin D receptor (VDR) was modeled based on the crystal structure of the retinoic acid receptor. The ligand binding pocket of our VDR model is spacious at the helix 11 site and confined at the β-turn site. The ligand 1α,25-dihydroxyvitamin D3 was assumed to be anchored in the ligand binding pocket with its side chain heading to helix 11 (site 2) and the A-ring toward the β-turn (site 1). Three residues forming hydrogen bonds with the functionally important 1α- and 25-hydroxyl groups of 1α,25-dihydroxyvitamin D3 were identified and confirmed by mutational analysis: the 1α-hydroxyl group is forming pincer-type hydrogen bonds with S237 and R274 and the 25-hydroxyl group is interacting with H397. Docking potential for various ligands to the VDR model was examined, and the results are in good agreement with our previous three-dimensional structure-function theory.

Reflections on the role and design of online dictionaries for specialised translation

This article is an updated and modified version of a Spanish article published in MonTi 6 (cf. Tarp 2014a). It deals with specialised translation dictionaries. Based on the principles of the function theory, it analyses the different phases and sub-phases of the translation process from a lexicographical perspective and shows that a translation dictionary should be much more than a mere bilingual dictionary if it really pretends to meet its users’ complex needs. Thereafter, it presents a global concept of a translation dictionary which includes various mono- and bilingual components in both language directions. Finally, the article discusses, by means of two concrete online projects, how this concept can be applied on the Internet in order to develop high-quality translation dictionaries with quick access to data that are still more adapted to the needs of each translator.

Evaluation and development of water wave theories for engineering application /

"November 1974."

On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities

Thesis (Ph.D.)--University of Washington, 2016-06

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Modeling Ultrafast Spectroscopy of the NADH Dimer: From UV-VIS to X-rays

Ultrafast pump-probe spectroscopy is a conceptually simple and versatile tool for resolving photoinduced dynamics in molecular systems. Due to the fast development of new experimental setups, such as synchrotron light sources and X-ray free electron lasers (XFEL), new spectral windows are becoming accessible. On the one hand, these sources have enabled scientist to access faster and faster time scales and to reach unprecedent insights into dynamical properties of matter. On the other hand, the complementarity of well-developed and novel techniques allows to study the same physical process from different points of views, integrating the advantages and overcoming the limitations of each approach. In this context, it is highly desirable to reach a clear understanding of which type of spectroscopy is more suited to capture a certain facade of a given photo-induced process, that is, to establish a correlation between the process to be unraveled and the technique to be used. In this thesis, I will show how computational spectroscopy can be a tool to establish such a correlation. I will study a specific process, which is the ultrafast energy transfer in the nicotinamide adenine dinucleotide dimer (NADH). This process will be observed in different spectral windows (from UV-VIS to X-rays), accessing the ability of different spectroscopic techniques to unravel the system evolution by means of state-of-the-art theoretical models and methodologies. The comparison of different spectroscopic simulations will demonstrate their complementarity, eventually allowing to identify the type of spectroscopy that is best suited to resolve the ultrafast energy transfer.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

Aspects of Iwasawa theory over function fields

"Vegeu el resum a l'inici del document del fitxer adjunt."

Unpacking the cognitive map: the parallel map theory of hippocampal function

In the parallel map theory, the hippocampus encodes space with 2 mapping systems. The bearing map is constructed primarily in the dentate gyrus from directional cues such as stimulus gradients. The sketch map is constructed within the hippocampus proper from positional cues. The integrated map emerges when data from the bearing and sketch maps are combined. Because the component maps work in parallel, the impairment of one can reveal residual learning by the other. Such parallel function may explain paradoxes of spatial learning, such as learning after partial hippocampal lesions, taxonomic and sex differences in spatial learning, and the function of hippocampal neurogenesis. By integrating evidence from physiology to phylogeny, the parallel map theory offers a unified explanation for hippocampal function.