<p>The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.</p>

Notre sujet de recherche est : “ comment obtenir la suite des reconfigurations que le système robotique doit faire pour qu'il se déplace globalement vers une destination ? ”. Comme nous le montrerons ce problème est très complexe. Nous verrons que ce travail qui a vite donné de bons résultats nous a permis de tester plusieurs méthodes : algorithmes réactifs, apprentissage supervisé et apprentissage à partir d'exemple. Nous montrerons également qu'au cours de ces simulations des problèmes inattendus sont apparus. Des blocages nous ont montré que la méthode utilisée pour faire les simulations était à discuter. C'est grâce à un grand nombre simulations que nous avons vu émerger deux types de problèmes. L'un lié à la nature de l'attracteur utilisé, l'autre lié à l'ordonnancement et à la dynamique des interactions. Nous définirons ces problèmes et expliquerons comment et pourquoi ils émergent. Deux axes seront proposés pour résoudre ces problèmes liés à l'émergence. L'un s'intéressera au type d'attracteur utilisé et proposera un système d'attraction aux propriétés différentes pour garantir un ordre sur l'espace. L'autre proposera une méthode pour permettre de garantir une politique d'ordonnancement quelque soit l'ordre dans lequel les calculs sont effectués dans les différents modules. L'ensemble de ces deux propriétés nous permettra de prouver la convergence du système robotique reconfigurable quelque soit la position de l'attracteur et quelque soit la configuration initiale du robot.

<p>The EU25 Member States’ GDP per capita levels converged in 1994-2005. Convergence occurred at an average speed of approximately 1.5 percent per year. In the first part of this paper unconditional convergence is analyzed by looking at both β- and σ-convergence and the performances of the catch-up economies are compared, discussed and related to the convergence definition. In a second stage, the catch-up performances are analyzed in relation to theory of economic integration. Substantial increases in labor productivity explain a great deal of the catch-up for poorer economies such as the Baltic states, while increases in employment have been relatively more important for the less poorer economies such as Spain, Portugal and Slovenia. Labor productivity is further elaborated and it is found that both FDIs and internal savings have been consistently higher for the catch-up economies than the non-catching-up economies. FDIs are also assumed to have indirect effects such as promoting incorporation of technology.</p>

<p>According to the different studies regarding customs unions and monetary unions, both these types of economic integration will lead to increased trade which in turn affects the price level.</p><p>In this study, the changes in the price levels across Europe are investigated in order to see if the changes can be attributed to the EMU and the Euro. By using the PPPs calculated by OECD based on the theory of Purchasing Power Parity price levels in different countries become comparable between the countries and over time. The result is that there seems to be a clear convergence towards an average European price level in the observed period 1980-2005.</p><p>In order to investigate if this convergence is an effect of the EMU a panel regression on relevant data is run and the result shows that there has been a convergence in the EMU-price level, but it can most likely not be attributed to the Euro, but other factors like for example increased degrees of openness.</p>

The problem of constructing a surface from the information provided by the Marr-Poggio theory of human stereo vision is investigated. It is argued that not only does this theory provide explicit boundary conditions at certain points in the image, but that the imaging process also provides implicit conditions on all other points in the image. This argument is used to derive conditions on possible algorithms for computing the surface. Additional constraining principles are applied to the problem; specifically that the process be performable by a local-support parallel network. Some mathematical tools, differential geometry, Coons surface patches and iterative methods of convergence, relevant to the problem of constructing the surface are outlined. Specific methods for actually computing the surface are examined.

Thesis (Ph.D. (Economics))--North-West University, Potchefstroom Campus, 2007.

Building on the work of Conrad Plaut and Valera Berestovskii regarding uniform spaces and the covering spectrum of Christina Sormani and Guofang Wei developed for geodesic spaces, the author defines and develops discrete homotopy theory for metric spaces, which can be thought of as a discrete analog of classical path-homotopy and covering space theory. Given a metric space, X, this leads to the construction of a collection of covering spaces of X - and corresponding covering groups - parameterized by the positive real numbers, which we call the [epsilon]-covers and the [epsilon]-groups. These covers and groups evolve dynamically as the parameter decreases, changing topological type at specific parameter values which depend on the topology and local geometry of X. This leads to the definition of a critical spectrum for metric spaces, which is the set of all values at which the topological type of the covers change. Several results are proved regarding the critical spectrum and its connections to topology and local geometry, particularly in the context of geodesic spaces, refinable spaces, and Gromov-Hausdorff limits of compact metric spaces. We investigate the relationship between the critical spectrum and covering spectrum in the case when X is geodesic, connections between the geometry of the [epsilon]-groups and the metric and topological structure of the [epsilon]-covers, as well as the behavior of the [epsilon]-covers and critical values under Gromov-Hausdorff convergence.

No description available.

No description available.

Recent advancements in iterative processing have allowed communication systems to perform close to capacity limits withmanageable complexity.For manychannels such as the AWGN and flat fading channels, codes that perform only a fraction of a dB from the capacity have been designed in the literature. In this dissertation, we will focus on the design and analysis of near-capacity achieving codes for another important class of channels, namely inter-symbol interference (ISI)channels. We propose various coding schemes such as low-density parity-check (LDPC) codes, parallel and serial concatenations for ISI channels when there is no spectral shaping used at the transmitter. The design and analysis techniques use the idea of extrinsic information transfer (EXIT) function matching and provide insights into the performance of different codes and receiver structures. We then present a coding scheme which is the concatenation of an LDPC code with a spectral shaping block code designed to be matched to the channel??s spectrum. We will discuss how to design the shaping code and the outer LDPC code. We will show that spectral shaping matched codes can be used for the parallel concatenation to achieve near capacity performance. We will also discuss the capacity of multiple antenna ISI channels. We study the effects of transmitter and receiver diversities and noisy channel state information on channel capacity.