Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Spatially-Explicit Testing of a General Aboveground Carbon Density Estimation Model in aWestern Amazonian Forest Using Airborne LiDAR

Mapping aboveground carbon density in tropical forests can support CO2 emissionmonitoring and provide benefits for national resource management. Although LiDAR technology has been shown to be useful for assessing carbon density patterns, the accuracy and generality of calibrations of LiDAR-based aboveground carbon density (ACD) predictions with those obtained from field inventory techniques should be intensified in order to advance tropical forest carbon mapping. Here we present results from the application of a general ACD estimation model applied with small-footprint LiDAR data and field-based estimates of a 50-ha forest plot in Ecuador?s Yasuní National Park. Subplots used for calibration and validation of the general LiDAR equation were selected based on analysis of topographic position and spatial distribution of aboveground carbon stocks. The results showed that stratification of plot locations based on topography can improve the calibration and application of ACD estimation using airborne LiDAR (R2 = 0.94, RMSE = 5.81 Mg?C? ha?1, BIAS = 0.59). These results strongly suggest that a general LiDAR-based approach can be used for mapping aboveground carbon stocks in western lowland Amazonian forests.

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Classification analytique de systèmes différentiels linéaires déployant une singularité irrégulière de rang de Poincaré 1

Cette thèse traite de la classification analytique du déploiement de systèmes différentiels linéaires ayant une singularité irrégulière. Elle est composée de deux articles sur le sujet: le premier présente des résultats obtenus lors de l'étude de la confluence de l'équation hypergéométrique et peut être considéré comme un cas particulier du second; le deuxième contient les théorèmes et résultats principaux. Dans les deux articles, nous considérons la confluence de deux points singuliers réguliers en un point singulier irrégulier et nous étudions les conséquences de la divergence des solutions au point singulier irrégulier sur le comportement des solutions du système déployé. Pour ce faire, nous recouvrons un voisinage de l'origine (de manière ramifiée) dans l'espace du paramètre de déploiement $\epsilon$. La monodromie d'une base de solutions bien choisie est directement reliée aux matrices de Stokes déployées. Ces dernières donnent une interprétation géométrique aux matrices de Stokes, incluant le lien (existant au moins pour les cas génériques) entre la divergence des solutions à $\epsilon=0$ et la présence de solutions logarithmiques autour des points singuliers réguliers lors de la résonance. La monodromie d'intégrales premières de systèmes de Riccati correspondants est aussi interprétée en fonction des éléments des matrices de Stokes déployées. De plus, dans le second article, nous donnons le système complet d'invariants analytiques pour le déploiement de systèmes différentiels linéaires $x^2y'=A(x)y$ ayant une singularité irrégulière de rang de Poincaré $1$ à l'origine au-dessus d'un voisinage fixé $\mathbb{D}_r$ dans la variable $x$. Ce système est constitué d'une partie formelle, donnée par des polynômes, et d'une partie analytique, donnée par une classe d'équivalence de matrices de Stokes déployées. Pour chaque valeur du paramètre $\epsilon$ dans un secteur pointé à l'origine d'ouverture plus grande que $2\pi$, nous recouvrons l'espace de la variable, $\mathbb{D}_r$, avec deux secteurs et, au-dessus de chacun, nous choisissons une base de solutions du système déployé. Cette base sert à définir les matrices de Stokes déployées. Finalement, nous prouvons un théorème de réalisation des invariants qui satisfont une condition nécessaire et suffisante, identifiant ainsi l'ensemble des modules.

Examining random number generators used in stochastic iteration algorithms

This paper investigates random number generators in stochastic iteration algorithms that require infinite uniform sequences. We take a simple model of the general transport equation and solve it with the application of a linear congruential generator, the Mersenne twister, the mother-of-all generators, and a true random number generator based on quantum effects. With this simple model we show that for reasonably contractive operators the theoretically not infinite-uniform sequences perform also well. Finally, we demonstrate the power of stochastic iteration for the solution of the light transport problem.

A Riemann solver for compressible flow of a real gas in a Lagrangian frame

An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a Lagrangian frame of reference.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

Sobre interações escalares e vetoriais na teoria de Duffin-Kemmer-Petiau

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evolução das modificações morfo-funcionais cardíacas no processo de adaptação crônica à insuficiência aórtica aguda experimental em ratos

Pós-graduação em Fisiopatologia em Clínica Médica - FMB

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.

Regional diversification and performance: Conceptualization and competing strategic objectives

This dissertation comprised of three essays provides justification for the need to pursue research on multinationality and performance with a more fine-grained approach. Essay one is a conceptual response to an article written by Jean-Francois Hennart in 2011 which questions the need and approach toward future research in this domain. I argue that internalization theory does not render multinationality and performance research meaningless and identify key areas where methodological enhancements can be made to strengthen our research findings with regard to Hennart's call for more content validity. Essay two responds to the need for more-fine grained research on the consequences of multinationality by introducing non-traditional measures of performance such as social and environmental performance and adopting a more theoretically relevant construct of regionalization to capture international diversification levels of the firm. Using data from the world's largest 600 firms (based on sales) derived from Bloomberg and the Directory of Corporate Affiliates; I employ general estimating equation analysis to account for the auto-correlated nature of the panel data alongside multivariate regression techniques. Results indicate that regionalization has a positive relationship with economic performance while it has a negative relationship with environmental and social performance outcomes, often referred to as the "Triple Bottom-Line" performance. Essay three builds upon the work in the previous essays by linking the aforementioned performance variables and sample to corporate reputation which has been shown to be a beneficial strategic asset. Using Structural Equation Modeling I explore economic, environmental and social signals as mediators on relationship between regionalization and firm reputation. Results indicate that these variables partially mediate a positive relationship between regionalization and firm reputation. While regionalization positively affects the reputation building signal of economic performance, it aids in reputation building by reducing environmental and social disclosure effects which interestingly impact reputation negatively. In conclusion, the dissertation submits opportunities for future research and contributes to research by demonstrating that regionalization affects performance, but the effect varies in accordance with the performance criterion and context. In some cases, regional diversification may produce competing or conflicting outcomes among the potential strategic objectives of the firm.

Development of a high-frequency surface-wave radar cross section model for icebergs

In this thesis, the first-order radar cross section (RCS) of an iceberg is derived and simulated. This analysis takes place in the context of a monostatic high frequency surface wave radar with a vertical dipole source that is driven by a pulsed waveform. The starting point of this work is a general electric field equation derived previ- ously for an arbitrarily shaped iceberg region surrounded by an ocean surface. The condition of monostatic backscatter is applied to this general field equation and the resulting expression is inverse Fourier transformed. In the time domain the excitation current of the transmit antenna is specified to be a pulsed sinusoid signal. The result- ing electric field equation is simplified and its physical significance is assessed. The field equation is then further simplified by restricting the iceberg's size to fit within a single radar patch width. The power received by the radar is calculated using this electric field equation. Comparing the received power with the radar range equation gives a general expression for the iceberg RCS. The iceberg RCS equation is found to depend on several parameters including the geometry of the iceberg, the radar frequency, and the electrical parameters of both the iceberg and the ocean surface. The RCS is rewritten in a form suitable for simulations and simulations are carried out for rectangularly shaped icebergs. Simulation results are discussed and are found to be consistent with existing research.

Regional Diversification and Performance: Conceptualization and Competing Strategic Objectives

This dissertation comprised of three essays provides justification for the need to pursue research on multinationality and performance with a more fine-grained approach. Essay one is a conceptual response to an article written by Jean-Francois Hennart in 2011 which questions the need and approach toward future research in this domain. I argue that internalization theory does not render multinationality and performance research meaningless and identify key areas where methodological enhancements can be made to strengthen our research findings with regard to Hennart’s call for more content validity. Essay two responds to the need for more-fine grained research on the consequences of multinationality by introducing non-traditional measures of performance such as social and environmental performance and adopting a more theoretically relevant construct of regionalization to capture international diversification levels of the firm. Using data from the world’s largest 600 firms (based on sales) derived from Bloomberg and the Directory of Corporate Affiliates; I employ general estimating equation analysis to account for the auto-correlated nature of the panel data alongside multivariate regression techniques. Results indicate that regionalization has a positive relationship with economic performance while it has a negative relationship with environmental and social performance outcomes, often referred to as the “Triple Bottom-Line” performance. Essay three builds upon the work in the previous essays by linking the aforementioned performance variables and sample to corporate reputation which has been shown to be a beneficial strategic asset. Using Structural Equation Modeling I explore economic, environmental and social signals as mediators on relationship between regionalization and firm reputation. Results indicate that these variables partially mediate a positive relationship between regionalization and firm reputation. While regionalization positively affects the reputation building signal of economic performance, it aids in reputation building by reducing environmental and social disclosure effects which interestingly impact reputation negatively. In conclusion, the dissertation submits opportunities for future research and contributes to research by demonstrating that regionalization affects performance, but the effect varies in accordance with the performance criterion and context. In some cases, regional diversification may produce competing or conflicting outcomes among the potential strategic objectives of the firm.