388 resultados para Lipschitz Mappings


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Mestrado em Engenharia Informática - Área de Especialização em Tecnologias do Conhecimento e Decisão

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Publicationes Mathematicae Debrecen

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Dissertation presented at Faculdade de Ciências e Tecnologia of Universidade Nova de Lisboa to obtain the Master degree in Electrical Engineering and Computer Science

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We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

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Many-core platforms are an emerging technology in the real-time embedded domain. These devices offer various options for power savings, cost reductions and contribute to the overall system flexibility, however, issues such as unpredictability, scalability and analysis pessimism are serious challenges to their integration into the aforementioned area. The focus of this work is on many-core platforms using a limited migrative model (LMM). LMM is an approach based on the fundamental concepts of the multi-kernel paradigm, which is a promising step towards scalable and predictable many-cores. In this work, we formulate the problem of real-time application mapping on a many-core platform using LMM, and propose a three-stage method to solve it. An extended version of the existing analysis is used to assure that derived mappings (i) guarantee the fulfilment of timing constraints posed on worst-case communication delays of individual applications, and (ii) provide an environment to perform load balancing for e.g. energy/thermal management, fault tolerance and/or performance reasons.

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Dissertation to obtain the Master degree in Electrical Engineering and Computer Science

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Dissertation to obtain the Master degree in Electrical Engineering and Computer Science

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Dissertação para obtenção do Grau de Doutor em Engenharia Electrotécnica e de Computadores

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Abstract Dataflow programs are widely used. Each program is a directed graph where nodes are computations and edges indicate the flow of data. In prior work, we reverse-engineered legacy dataflow programs by deriving their optimized implementations from a simple specification graph using graph transformations called refinements and optimizations. In MDE-speak, our derivations were PIM-to-PSM mappings. In this paper, we show how extensions complement refinements, optimizations, and PIM-to-PSM derivations to make the process of reverse engineering complex legacy dataflow programs tractable. We explain how optional functionality in transformations can be encoded, thereby enabling us to encode product lines of transformations as well as product lines of dataflow programs. We describe the implementation of extensions in the ReFlO tool and present two non-trivial case studies as evidence of our work’s generality

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Dissertação de mestrado em Engenharia Industrial

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In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

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R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

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We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

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We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

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The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.