Besov spaces and the Laplacian on fractal H-sets

Nesta tese são estudados espaços de Besov de suavidade generalizada em espaços euclidianos, numa classe de fractais designados conjuntos-h e em estruturas abstractas designadas por espaços-h. Foram obtidas caracterizações e propriedades para estes espaços de funções. Em particular, no caso de espaços de Besov em espaços euclidianos, foram obtidas caracterizações por diferenças e por decomposições em átomos não suaves, foi provada uma propriedade de homogeneidade e foram estudados multiplicadores pontuais. Para espaços de Besov em conjuntos-h foi obtida uma caracterização por decomposições em átomos não suaves e foi construído um operador extensão. Com o recurso a cartas, os resultados obtidos para estes espaços de funções em fractais foram aplicados para definir e trabalhar com espaços de Besov de suavidade generalizada em estruturas abstractas. Nesta tese foi também estudado o laplaciano fractal, considerado a actuar em espaços de Besov de suavidade generalizada em domínios que contêm um conjunto-h fractal. Foram obtidos resultados no contexto de teoria espectral para este operador e foi estudado, à custa deste operador, um problema de Dirichlet fractal no contexto de conjuntos-h.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Multifractal portrayal of the Swiss population

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

The European dimension for the mouse genome mutagenesis program.

The European Mouse Mutagenesis Consortium is the European initiative contributing to the international effort on functional annotation of the mouse genome. Its objectives are to establish and integrate mutagenesis platforms, gene expression resources, phenotyping units, storage and distribution centers and bioinformatics resources. The combined efforts will accelerate our understanding of gene function and of human health and disease.

Automatic Structure Generation using Genetic Programming and Fractal Geometry

Three dimensional model design is a well-known and studied field, with numerous real-world applications. However, the manual construction of these models can often be time-consuming to the average user, despite the advantages o ffered through computational advances. This thesis presents an approach to the design of 3D structures using evolutionary computation and L-systems, which involves the automated production of such designs using a strict set of fitness functions. These functions focus on the geometric properties of the models produced, as well as their quantifiable aesthetic value - a topic which has not been widely investigated with respect to 3D models. New extensions to existing aesthetic measures are discussed and implemented in the presented system in order to produce designs which are visually pleasing. The system itself facilitates the construction of models requiring minimal user initialization and no user-based feedback throughout the evolutionary cycle. The genetic programming evolved models are shown to satisfy multiple criteria, conveying a relationship between their assigned aesthetic value and their perceived aesthetic value. Exploration into the applicability and e ffectiveness of a multi-objective approach to the problem is also presented, with a focus on both performance and visual results. Although subjective, these results o er insight into future applications and study in the fi eld of computational aesthetics and automated structure design.

Unveiling the Influence of Consumer Wine Appreciation Dimension on Purchasing Behavior

Consumption values and different usage situations have received extensive interest from scholars; however, there is a lack of understanding regarding how these two constructs interact when it comes to the purchase decisions of consumers. This study examines the relationship between consumption values, consumption situations, and consumers’ purchasing decisions in terms of their willingness to pay and the purchase quantity. First of all, my model proposes that all four consumption values and different situations have a positive effect on consumers’ willingness to pay as well as the quantity they purchase. It also proposes that varying usage situations moderate the effect of consumption values on consumers’ purchasing decisions. In my conceptual model, I have also integrated the epistemic and conditional values where there is a gap in the existing literature. Prior literature has isolated the consumption values when studying how they affect consumer behavior and has not examined how consumption situations moderate the relationship between consumption values and purchasing decisions. Also, the existing literature has mostly focused on how consumption values affect purchase intentions, brand loyalty, or satisfaction, whereas my study focuses on purchasing decisions. For my study, the participants were randomly chosen from the general wine consumer population and the age range was between 20 and 75, which included 83 male respondents and 119 female respondents. The data received from my respondents support my hypotheses for the model. In my final chapter, I discuss the theoretical and managerial implications as well as suggestions for future research.

"I'm Your Biggest Fan, I'll Follow You ... " Lady Gaga, Little Monsters and the Religious Dimension of Fandom in Pop Music

This thesis examines the religious dimension of fandom in popular music, taking as an object of reflection Lady Gaga and her fans. I combine fan studies with theories of immanence as well as Deleuze and Guattari's notion of the process of becoming, and provide a theoretical reading of the relationship between Lady Gaga and her most fervent fans, the 'little monsters.' Both fandom and religion promise a stable sense of identity and authentic community to devotees. Performing deconstructive discourse analysis on three of Lady Gaga's music videos, I demonstrate how fandom, like organized religion, can simultaneously be an emancipatory practice and a practice that seeks to deny individual subjects their agency. This thesis provides a new theoretical framework for understanding fandom, and illustrates how the purported benefits of both fandom and religion can only be gained when the figureheads of each group are symbolically destroyed by the members themselves.

Estudio de microestructuras dendríticas mediante análisis fractal

Tesis (Maestría en Ciencias de la Ingeniería Mecánica con Especialidad en Materiales) UANL

Medición de la dimensión fractal de la microestructura de aceros

Tesis (Maestría en Ciencias de la Ingeniería Mecánica, con especialidad en Materiales). U. A. N. L.