Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Peirce's mathematical-logical approach to discrete collections and the premonition of continuity

According to Peirce one of the most important philosophical problems is continuity. Consequently, he set forth an innovative and peculiar approach in order to elucidate at once its mathematical and metaphysical challenges through proper non-classical logical reasoning. I will restrain my argument to the definition of the different types of discrete collections according to Peirce, with a special regard to the phenomenon called premonition of continuity (Peirce, 1976, Vol. 3, p. 87, c. 1897). © 2012 Copyright Taylor and Francis Group, LLC.

Absolute continuity and existence of solutions to dynamic inclusions in time scales

We provide some properties for absolutely continuous functions in time scales. Then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question. We also introduce the so called Euler solution to dynamical systems in time scales and prove its existence. A combination of the existence of Euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty, compact, convex and has closed graph. © 2012 Springer-Verlag.

ECLAC: forty years of continuity with change

Discurso inaugural del 22 periodo de sesiones de la CEPAL efectuado por el senor Gert Rosenthal, en el cual se refiere en especial al papel pasado, presente y futuro de la Comision en el desarrollo economico y social de la region.

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Support infrastructures for multimedia services with guaranteed continuity and QoS

Advances in wireless networking and content delivery systems are enabling new challenging provisioning scenarios where a growing number of users access multimedia services, e.g., audio/video streaming, while moving among different points of attachment to the Internet, possibly with different connectivity technologies, e.g., Wi-Fi, Bluetooth, and cellular 3G. That calls for novel middlewares capable of dynamically personalizing service provisioning to the characteristics of client environments, in particular to discontinuities in wireless resource availability due to handoffs. This dissertation proposes a novel middleware solution, called MUM, that performs effective and context-aware handoff management to transparently avoid service interruptions during both horizontal and vertical handoffs. To achieve the goal, MUM exploits the full visibility of wireless connections available in client localities and their handoff implementations (handoff awareness), of service quality requirements and handoff-related quality degradations (QoS awareness), and of network topology and resources available in current/future localities (location awareness). The design and implementation of the all main MUM components along with extensive on the field trials of the realized middleware architecture confirmed the validity of the proposed full context-aware handoff management approach. In particular, the reported experimental results demonstrate that MUM can effectively maintain service continuity for a wide range of different multimedia services by exploiting handoff prediction mechanisms, adaptive buffering and pre-fetching techniques, and proactive re-addressing/re-binding.

Continuity and Change in New Products

This doctoral dissertation is triggered by an emergent problem: how can firms reinvent themselves? Continuity- and change-oriented decisions fundamentally shape overtime the activities and potential revenues of organizations and other adaptive systems, but both types of actions draw upon limited resources and rely on different organizational routines and capabilities. Most organizations appear to have difficulties in making tradeoffs, so that it is easier to overinvest in one of them than to successfully achieve a mixture of both. Nevertheless, theory and empirical evidence suggest that too little of either may reduce performance, indicating a need to learn more about how organizations reconcile these tensions. In the first paper, I moved from the consideration that rapid changes in competitive environments increasingly require firms to be “ambidextrous” implementing organizational mechanisms and structures that allow continuity- and change-oriented activities to be engaged at the same time. More specifically, I show that continuity- and change-related decisions can’t be confined either inside or outside the firm, but span overtime across distinct decision domains located within and beyond the organizational boundaries. Reconciling static and dynamic perspectives of ambidexterity, I conceptualize a firm’s strategy as a bundle of decisions about product attributes and components of the production team, proposing a multidimensional and dynamic model of structural ambidexterity that explains why and how firms could manage conflicting pressures for continuity and change in the context of new products. In the second study I note how rigorous systematic evidence documenting the success of ambidextrous organizations is lacking, and there has been very little investigation of how firms deal with continuity and change in new products. How to manage the transition form a successful product to another? What to change and what to keep? Incumbents that deal with series of products over time need to update their offerings in order to have the most relevant attributes to prospect clients without disappoint the current customer base. They need to both match and anticipate consumers’ preferences, blending something old with something new to satisfy the current demand and enlarge the herd by appealing to newer audiences. This paper contributes to strategic renewal and ambidexterity-related research with the first empirically assessment of a positive consumer response to ambidexterity in new products. Also, this study provides a practical method to monitor overtime the degree to which a brand or a firm is continuity- or change- oriented and evaluate different strategy profiles across two decision domains that play a pivotal role in new products: product attributes and components of the production team.

Compulsive-Like Behaviors of Typical Development: A Question of Their Nature and Continuity with Obsessive-Compulsive Disorder

OBJECTIVE: To investigate compulsive-like behaviors (CLB) of typical development: how they relate to the obsessions and compulsions of obsessive-compulsive disorder (OCD); and the implication of their lingering past 6 years of age (i.e., past their normative, 2-to-5 year, drop). CONCLUSIONS: Findings suggest that normative CLB exist on a continuum (with regard to both symptomatology and functional difficulties) with clinical obsessions and compulsions. With normative repetitive behaviors predicting behavioral perseveration among typically developing individuals aged 6 to 17 years, the present study also suggests that, even in a non-clinical sample, some levels of CLB are maladaptive in middle childhood through adolescence. While studies to date have evaded investigation of high and low CLB in relation to OCD, this latter finding contributes to the growing emphasis upon continuity between typical and atypical development.