BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Fred: An approach to generating real, correct, reusable programs from proofs

In this paper we describe our system for automatically extracting "correct" programs from proofs using a development of the Curry-Howard process. Although program extraction has been developed by many authors, our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin's technique to reduce higher-order logic to many-sorted (first-order) logic; 2. the free use of new rules for induction subject to certain conditions; 3. the extensive use of previously programmed (total, recursive) functions; 4. the use of templates to make the reasoning much closer to normal mathematical proofs and 5. a conceptual distinction between the computational type theory (for representing programs)and the logical type theory (for reasoning about programs). As an example of our system we give a constructive proof of the well known theorem that every graph of even parity, which is non-trivial in the sense that it does not consist of isolated vertices, has a cycle. Given such a graph as input, the extracted program produces a cycle as promised.

Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

QoS-aware model driven architecture through the UML and CIM

The specification of Quality of Service (QoS) constraints over software design requires measures that ensure such requirements are met by the delivered product. Achieving this goal is non-trivial, as it involves, at least, identifying how QoS constraint specifications should be checked at the runtime. In this paper we present an implementation of a Model Driven Architecture (MDA) based framework for the runtime monitoring of QoS properties. We incorporate the UML2 superstructure and the UML profile for Quality of Service to provide abstract descriptions of component-and-connector systems. We then define transformations that refine the UML2 models to conform with the Distributed Management Taskforce (DMTF) Common Information Model (CIM) (Distributed Management Task Force Inc. 2006), a schema standard for management and instrumentation of hardware and software. Finally, we provide a mapping the CIM metamodel to a .NET-based metamodel for implementation of the monitoring infrastructure utilising various .NET features including the Windows Management Instrumentation (WMI) interface.

Redistribution with ex-ante unobserved choice

Introducing dynamics to Mirrlees' (1971) optimal taxation model creates a whole new set of issues that are only starting to be investigated in the literature. When choices are made before one's realizing her productivity incentive constraints ought to be defined as a function of more complex strategies than in the static case. 80 far, all work has assumed that these choices are observable and can be contracted upon by the government. Here we investigate choices that : i) are not observed, andj ii) affect preferences conditional Oil the realization of types. In the simplest possible model where a non-trivial filtration is incorporated we show how these two characteristics make it necessary for IC constraints to be defined in terms of strategies rather than pure announcements. Tax prescriptions are derived, and it is shown that they bear some resemblance to classic optimal taxation results. We are able to show that in the most 'natural' cases return on capital ought to be taxed . However, we also show that the uniform taxation prescription of Atkinson and Stiglitz fails to hold, in general.

Custos de ajustamento e a dinâmica da estrutura de capital em empresas brasileiras

Diversos estudos de Finanças Corporativas consideram os custos associados aos ajustes da estrutura de capital das empresas irrelevantes tanto na forma quanto em magnitude. Este estudo analisou empiricamente a influência dos custos de ajustamento na dinâmica dos ajustes da estrutura de capital de empresas brasileiras de capital aberto no período de 1999 a 2007. A alavancagem foi abordada sob três diferentes cenários, considerando a presença de custos fixos, custos proporcionais e por uma composição de custos fixos e proporcionais através de simulações utilizando um modelo reduzido da estrutura de capital. Em seguida a análise não paramétrica da amostra revelou que as empresas apresentam um comportamento dinâmico em suas decisões de financiamento para o ajuste da estruturas de capital, mas que não se revelou contínuo. A utilização de um modelo de duration mostrou-se adequado para mensurar o intervalo de tempo entre os ajustes da estrutura de capital das empresas. Os resultados são extremamente relevantes e suportam a teoria de um comportamento de rebalanceamento dinâmico pelas empresas de suas estruturas de capital em torno de um intervalo ótimo. Entretanto os ajustes não ocorrem de forma imediata e a persistência de choques à estrutura de capital deve-se em sua maior parte aos custos associados aos ajustes do que a uma possível indiferença à estrutura de capital. . Este trabalho constitui-se como pioneiro no mercado brasileiro acerca dos custos de ajustamento da estrutura de capital e abre espaço para a discussão do comportamento ótimo em torno da estrutura de capital de empresas nacionais.

The private memory of aggregate shocks

Em economias caracterizadas por choques agregados e privados, mostramos que a alocação ótima restrita pode depender de forma não-trivial dos choques agregados. Usando versões dos modelos de Atkeson e Lucas (1992) e Mirrlees (1971) de dois períodos, é mostrado que a alocação ótima apresenta memória com relação aos choques agregados mesmo eles sendo i.i.d. e independentes dos choques individuais, quando esses últimos choques não são totalmente persistentes. O fato de os choques terem efeitos persistentes na alocação mesmo sendo informação pública, foi primeiramente apresentado em Phelan (1994). Nossas simulações numéricas indicam que esse não é um resultado pontual: existe uma relação contínua entre persistência de tipos privados e memória do choque agregado.

Psicologia social, ideológica e meta-ideológica: (psicogênese e sociogênese no modelo dialético)

O presente estudo propõe uma interpretação da Psicologia Social como expressão da relação homem/meio, baseada no modelo dialético genético-estrutural Piagetano. É conceituada uma interdependência entre diferentes níveis de análise teórica e uma continuidade do mais simples ao complexo, mantendo-se a autonomia relativa, em cada nível que, com suas próprias leis, obedecerá ao sistema global da organização vital: níveis biológicos, psicológicos e sociológicos encadeiam-se, sem que se possa definir um limite estrito entre eles. Supera-se assim o problema metodológico de abstração de níveis que leva a consideráveis distorções, especialmente quando se abstrai o nível político-social. Psicologia Social será o estudo da ação que uma estrutura social provoca no indivíduo e a ação recíproca que o indivíduo exerce sobre a estrutura social: o sujeito participa ativamente, em grupo, da construção da estrutura que sobre ele atua. Frente à abordagem psicossocial dominante, empírico-analítica e à abordagem alternativa, histórico-social, e introduzida uma visão interacionista que integra como complementares posições conflitantes, sendo criticadas teorias que pretendem reduzir o comportamento humano ao meio ou ao sujeito. É proposta uma teoria psicobiológica da relação homem/meio que definira o grau de desenvolvimento atingido pelo indivíduo e grupo como função da interação permitida: se o contexto for repressor, ocorrera uma atualização empobrecida de fenótipos culturais. O psicólogo social deverá ter um enfoque do desenvolvimento do indivíduo e sociedade, para poder atuar de forma politicamente relevante. A ideologia ê interpretada como expressa0 de uma função humana mais geral, a função simbólica e será sempre dependente da autorregularão atingida pelo grupo em um contexto sócio-político específico. Como uma ação concreta sempre é ideológica por sua práxis, um nível meta-ideológico só será atingido através da atuação num nível ideológico; apenas através da pesquisa psico e sociogenética se atingirá um dado não-ideológico.

Yet another reason to tax goods

When, in a dynamic model, choices by an agent : i) are not observed, and; ii) affect preferences conditional on the realization of types, new and unexpected features come up in Mirrlees’ (1971) optimal taxation frame- work. In the simplest possible model where a non-trivial filtration may be incorporated, we show how these two characteristics make it neces- sary for IC constraints to be defined in terms of strategies rather than pure announcements. Tax prescriptions are derived, and we are able to show that uniform taxation prescription of Atkinson and Stiglitz fails to hold, in general. Clean results regarding capital income taxation are not easy to come about because usual assumption on preferences do not allow for determining which constraints bind at the optimum. However, in the most ’natural’ cases, we show that return on capital ought to be taxed.

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

Elétrons fortemente correlacionados na vizinhança de uma transição de fase quântica

The aim of this work is to derive theWard Identity for the low energy effective theory of a fermionic system in the presence of a hyperbolic Fermi surface coupled with a U(1) gauge field in 2+1 dimensions. These identities are important because they establish requirements for the theory to be gauge invariant. We will see that the identity associated Ward Identity (WI) of the model is not preserved at 1-loop order. This feature signalizes the presence of a quantum anomaly. In other words, a classical symmetry is broken dynamically by quantum fluctuations. Furthermore, we are considering that the system is close to a Quantum Phase Transitions and in vicinity of a Quantum Critical Point the fermionic excitations near the Fermi surface, decay through a Landau damping mechanism. All this ingredients need to be take explicitly to account and this leads us to calculate the vertex corrections as well as self energies effects, which in this way lead to one particle propagators which have a non-trivial frequency dependence

BSmart: desenvolvimento rigoroso de aplicações Java Card com base no método formal B

Java Card technology allows the development and execution of small applications embedded in smart cards. A Java Card application is composed of an external card client and of an application in the card that implements the services available to the client by means of an Application Programming Interface (API). Usually, these applications manipulate and store important information, such as cash and confidential data of their owners. Thus, it is necessary to adopt rigor on developing a smart card application to improve its quality and trustworthiness. The use of formal methods on the development of these applications is a way to reach these quality requirements. The B method is one of the many formal methods for system specification. The development in B starts with the functional specification of the system, continues with the application of some optional refinements to the specification and, from the last level of refinement, it is possible to generate code for some programming language. The B formalism has a good tool support and its application to Java Card is adequate since the specification and development of APIs is one of the major applications of B. The BSmart method proposed here aims to promote the rigorous development of Java Card applications up to the generation of its code, based on the refinement of its formal specification described in the B notation. This development is supported by the BSmart tool, that is composed of some programs that automate each stage of the method; and by a library of B modules and Java Card classes that model primitive types, essential Java Card API classes and reusable data structures