Digit systems over commutative rings

Let epsilon be a commutative ring with identity and P is an element of epsilon[x] be a polynomial. In the present paper we consider digit representations in the residue class ring epsilon[x]/(P). In particular, we are interested in the question whether each A is an element of epsilon[x]/(P) can be represented modulo P in the form e(0)+ e(1)x + ... + e(h)x(h), where the e(i) is an element of epsilon[x]/(P) are taken from a fixed finite set of digits. This general concept generalizes both canonical number systems and digit systems over finite fields. Due to the fact that we do not assume that 0 is an element of the digit set and that P need not be monic, several new phenomena occur in this context.

THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multi-task control strategy for grid-tied inverters based on conservative power theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Theoretical study of molecular and electronic structures of 5(1) knot systems: two-layered ONIOM calculations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Artificial immune networks Copt-aiNet and Opt-aiNet applied to the reconfiguration problem of radial electrical distribution systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hilbert space of curved βγ systems on quadric cones

We clarify the structure of the Hilbert space of curved βγ systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.

Planning “Discrete” Movements Using a Continuous System: Insights from a Dynamic Field Theory of Movement Preparation

The timed-initiation paradigm developed by Ghez and colleagues (1997) has revealed two modes of motor planning: continuous and discrete. Continuous responding occurs when targets are separated by less than 60° of spatial angle, and discrete responding occurs when targets are separated by greater than 60°. Although these two modes are thought to reflect the operation of separable strategic planning systems, a new theory of movement preparation, the Dynamic Field Theory, suggests that two modes emerge flexibly from the same system. Experiment 1 replicated continuous and discrete performance using a task modified to allow for a critical test of the single system view. In Experiment 2, participants were allowed to correct their movements following movement initiation (the standard task does not allow corrections). Results showed continuous planning performance at large and small target separations. These results are consistent with the proposal that the two modes reflect the time-dependent “preshaping” of a single planning system.

Parental Ethnotheories of Child Development: Looking Beyond Independence and Individualism in American Belief Systems

Over the past several decades, the topic of child development in a cultural context has received a great deal of theoretical and empirical investigation. Investigators from the fields of indigenous and cultural psychology have argued that childhood is socially and historically constructed, rather than a universal process with a standard sequence of developmental stages or descriptions. As a result, many psychologists have become doubtful that any stage theory of cognitive or socialemotional development can be found to be valid for all times and places. In placing more theoretical emphasis on contextual processes, they define culture as a complex system of common symbolic action patterns (or scripts) built up through everyday human social interaction by means of which individuals create common meanings and in terms of which they organize experience. Researchers understand culture to be organized and coherent, but not homogenous or static, and realize that the complex dynamic system of culture constantly undergoes transformation as participants (adults and children) negotiate and re-negotiate meanings through social interaction. These negotiations and transactions give rise to unceasing heterogeneity and variability in how different individuals and groups of individuals interpret values and meanings. However, while many psychologists—both inside and outside the fields of indigenous and cultural psychology–are now willing to give up the idea of a universal path of child development and a universal story of parenting, they have not necessarily foreclosed on the possibility of discovering and describing some universal processes that underlie socialization and development-in-context. The roots of such universalities would lie in the biological aspects of child development, in the evolutionary processes of adaptation, and in the unique symbolic and problem-solving capacities of the human organism as a culture-bearing species. For instance, according to functionalist psychological anthropologists, shared (cultural) processes surround the developing child and promote in the long view the survival of families and groups if they are to demonstrate continuity in the face of ecological change and resource competition, (e.g. Edwards & Whiting, 2004; Gallimore, Goldenberg, & Weisner, 1993; LeVine, Dixon, LeVine, Richman, Leiderman, Keefer, & Brazelton, 1994; LeVine, Miller, & West, 1988; Weisner, 1996, 2002; Whiting & Edwards, 1988; Whiting & Whiting, 1980). As LeVine and colleagues (1994) state: A population tends to share an environment, symbol systems for encoding it, and organizations and codes of conduct for adapting to it (emphasis added). It is through the enactment of these population-specific codes of conduct in locally organized practices that human adaptation occurs. Human adaptation, in other words, is largely attributable to the operation of specific social organizations (e.g. families, communities, empires) following culturally prescribed scripts (normative models) in subsistence, reproduction, and other domains [communication and social regulation]. (p. 12) It follows, then, that in seeking to understand child development in a cultural context, psychologists need to support collaborative and interdisciplinary developmental science that crosses international borders. Such research can advance cross-cultural psychology, cultural psychology, and indigenous psychology, understood as three sub-disciplines composed of scientists who frequently communicate and debate with one another and mutually inform one another’s research programs. For example, to turn to parental belief systems, the particular topic of this chapter, it is clear that collaborative international studies are needed to support the goal of crosscultural psychologists for findings that go beyond simply describing cultural differences in parental beliefs. Comparative researchers need to shed light on whether parental beliefs are (or are not) systematically related to differences in child outcomes; and they need meta-analyses and reviews to explore between- and within-culture variations in parental beliefs, with a focus on issues of social change (Saraswathi, 2000). Likewise, collaborative research programs can foster the goals of indigenous psychology and cultural psychology and lay out valid descriptions of individual development in their particular cultural contexts and the processes, principles, and critical concepts needed for defining, analyzing, and predicting outcomes of child development-in-context. The project described in this chapter is based on an approach that integrates elements of comparative methodology to serve the aim of describing particular scenarios of child development in unique contexts. The research team of cultural insiders and outsiders allows for a look at American belief systems based on a dialogue of multiple perspectives.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Encapsulation of small magnetic clusters in fullerene cages: A density functional theory investigation within van der Waals corrections

The encapsulation of magnetic transition-metal (TM) clusters inside carbon cages (fullerenes, nanotubes) has been of great interest due to the wide range of applications, which spread from medical sensors in magnetic resonance imaging to photonic crystals. Several theoretical studies have been reported; however, our atomistic understanding of the physical properties of encapsulated magnetic TM 3d clusters is far from satisfactory. In this work, we will report general trends, derived from density functional theory within the generalized gradient approximation proposed by Perdew, Burke, and Ernzerhof (PBE), for the encapsulation properties of the TMm@C-n (TM = Fe, Co, Ni; m = 2-6, n = 60,70,80,90) systems. Furthermore, to understand the role of the van der Waals corrections to the physical properties, we employed the empirical Grimme's correction (PBE + D2). We found that both PBE and PBE + D2 functionals yield almost the same geometric parameters, magnetic and electronic properties, however, PBE + D2 strongly enhances the encapsulation energy. We found that the center of mass of the TMm clusters is displaced towards the inside C-n surfaces, except for large TMm clusters (m = 5 and 6). For few cases, e. g., Co-4 and Fe-4, the encapsulation changes the putative lowest-energy structure compared to the isolated TMm clusters. We identified few physical parameters that play an important role in the sign and magnitude of the encapsulation energy, namely, cluster size, fullerene equatorial diameter, shape, curvature of the inside C-n surface, number of TM atoms that bind directly to the inside C-n surface, and the van der Waals correction. The total magnetic moment of encapsulated TMm clusters decreases compared with the isolated TMm clusters, which is expected due to the hybridization of the d-p states, and strongly depends on the size and shape of the fullerene cages.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.