REALIZING PROFINITE REDUCED SPECIAL GROUPS

Special groups are an axiomatization of the algebraic theory of quadratic forms over fields. It is known that any finite reduced special group is the special group of some field. We show that any special group that is the projective limit of a projective system of finite reduced special groups is also the special group of some field.

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.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Elevers läsvanor : En kvalitativ studie av fyra fordonselevers läsvanor

The following study was conducted at an upper secondary school in Sweden and attempts to explore the question of what influences male pupils’ reading habits. Many quantitative international studies, including PISA, PIRLS and IEA Reading Literacy, have sought to answer this question, but only partially succeeded due to the limitations of their methods. Therefore, this study seeks to explore this question in more depth using qualitative methods, including interviews and classroom observations, but also minor tests. Two facts which the previously mentioned international studies have found is that boys and particularly immigrant boys tend to have worse reading results than their counterparts. It is therefore the aim of this study to study four male students in upper secondary school; of which two are native Swedes and the other two are unaccompanied refugee children; one from Afghanistan and the other from Morocco. The findings of this study are as follows. Firstly, necessity was found to be the single most important factor for the reading habits of these four pupils; especially the two refugees. Both refugees learnt to read under harsh circumstances in madrassas in their respective home countries. Moreover, the Moroccan pupil learnt to speak and read Spanish fluently during his seven years as a homeless child. Furthermore, in the absence of necessity, interest was found to be decisive in determining the pupils’ reading habits. In addition to this, the study theorizes that an interest in reading generally arises before the ability to read and not vice versa. However, teachers can in fact affect their pupils’ reading habits even in upper secondary school.

Extraction of structured programs from specification proofs

We present a method using an extended logical system for obtaining programs from specifications written in a sublanguage of CASL. These programs are “correct” in the sense that they satisfy their specifications. The technique we use is to extract programs from proofs in formal logic by techniques due to Curry and Howard. The logical calculus, however, is novel because it adds structural rules corresponding to the standard ways of modifying specifications: translating (renaming), taking unions, and hiding signatures. Although programs extracted by the Curry-Howard process can be very cumbersome, we use a number of simplifications that ensure that the programs extracted are in a language close to a standard high-level programming language. We use this to produce an executable refinement of a given specification and we then provide a method for producing a program module that maximally respects the original structure of the specification. Throughout the paper we demonstrate the technique with a simple example.

Study of the audio coding algorithm of the MPEG-4 AAC standard and comparison among implementations of modules of the algorithm

Audio coding is used to compress digital audio signals, thereby reducing the amount of bits needed to transmit or to store an audio signal. This is useful when network bandwidth or storage capacity is very limited. Audio compression algorithms are based on an encoding and decoding process. In the encoding step, the uncompressed audio signal is transformed into a coded representation, thereby compressing the audio signal. Thereafter, the coded audio signal eventually needs to be restored (e.g. for playing back) through decoding of the coded audio signal. The decoder receives the bitstream and reconverts it into an uncompressed signal. ISO-MPEG is a standard for high-quality, low bit-rate video and audio coding. The audio part of the standard is composed by algorithms for high-quality low-bit-rate audio coding, i.e. algorithms that reduce the original bit-rate, while guaranteeing high quality of the audio signal. The audio coding algorithms consists of MPEG-1 (with three different layers), MPEG-2, MPEG-2 AAC, and MPEG-4. This work presents a study of the MPEG-4 AAC audio coding algorithm. Besides, it presents the implementation of the AAC algorithm on different platforms, and comparisons among implementations. The implementations are in C language, in Assembly of Intel Pentium, in C-language using DSP processor, and in HDL. Since each implementation has its own application niche, each one is valid as a final solution. Moreover, another purpose of this work is the comparison among these implementations, considering estimated costs, execution time, and advantages and disadvantages of each one.

Divisia indexes, money and welfare

We suggest the use of a particular Divisia index for measuring welfare losses due to interest rate wedges and in‡ation. Compared to the existing options in the literature: i) when the demands for the monetary assets are known, closed-form solutions for the welfare measures can be obtained at a relatively lower algebraic cost; ii) less demanding integrability conditions allow for the recovery of welfare measures from a larger class of demand systems and; iii) when the demand speci…cations are not known, using an index number entitles the researcher to rank di¤erent vectors of opportunity costs directly from market observations. We use two examples to illustrate the method.

Duas vertentes da ontogênese da linguagem no desenvolvimento cognitivo

Este estudo pretende trazer uma contribuição à discussão da relação linguagem-cognição, através do exame de um aspecto restrito do problema: a hipótese de uma base cognitiva para aquisição de linguagem. O modelo teórico piagetiano é analisado em sua explicação da ontogenese da linguagem como resultante das construções da inteligência sensório-motora. Alguns de seus aspectos são questionados, a possibilidade de sua explicitação em forma de hipótese verificável é examinada e a literatura é analisada em busca de evidências relevantes. A principal lacuna constatada é a visão de linguagem restrita a aspectos de desempenho, sendo levado em conta apenas o começo da emissão de palavras na quase totalidade das pesquisas. Ainda dentro de uma perspectiva construtivista, o esboço de um novo modelo teórico é proposto, incluindo a discussão da ontogenese da compreensão de linguagem. Hipóteses decorrentes da proposta teórica, especialmente a de início da possibilidade de tratar o signo linguístico antes do estágio VI, são formuladas e verificadas por pesquisa empírica. Esta inclui um estudo longitudinal e outro transversal do desenvolvimento linguístico e cognitivo de 45 crianças entre 8 e 18 meses. O desenvolvimento da compreensão é comparado em diversos aspectos ao da produção ou fala. Verifica-se que o primeiro começa mais cedo, é mais rápido e atinge um vocabulário maior e um nível mais complexo na faixa etária estudada. Há evidências ainda de diferenças no papel da imitação na construção do vocabulário nas duas vertentes. Observa-se um início de resposta mais generalizada e sistemática à linguagem a partir de nove meses, ocasião em que a criança se mostra capaz de coordenação de reações circulares secundárias e quando consegue reconstruir mentalmente um objeto invisível a partir de uma fração visível. Considera-se que esta resposta já envolve a decodificação de signos e a diferenciação significante-significado, numa etapa preliminar de um processo evolutivo que se entrelaça com a formação de conceitos. Os dados nao permitem a identificação de prê-requisitos cognitivos para aquisição de liguagem, mas dois aspectos podem ser destacados como correlatos do início do processo de compartilhar o signo linguístico: a possibilidade da criança compreender que tem um nome e responder a ele e uma intencionalidade primitiva. Os resultados apoiam as hipóteses formuladas e sugerem que as construções finais do período sensório-motor não são condições necessárias para aquisição de linguagem e que esta não ê consequência direta do desenvolvimento cognitivo. Novos estudos são necessários para suprir as limitações desta pesquisa e verificação das implicações decorrentes dos resultados obtidos.

On the construction of explicit exponential based schemes for Stiff SDEs

Trabalho apresentado Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-14), Halle, 7-11 Sep 2015

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Sobre uma cultura do mal-estar com a política

The current dissertation has as its main object of study the malaise with politics phenomenon. To comprehend it, is carried out in this work a inquiry, in different stages of analysis, based in the empirical data raised by the research Os Processos Sociais de Recepção do Horário Gratuito de Propaganda Eleitoral , made by the Grupo de Estudos Mídia e Poder, of the Universidade Federal do Rio Grande do Norte, during the local elections of 2004 in the city of Natal. Based in the focus group technique, such research raised an ample set of information about the decoding process of the electoral television programs, made by six different groups of citizens from the popular classes. Beginning from the presuppose which such process is influenced by the representations about politics made by those subjects, we use that set of empirical information to inquiry not only the decoding, but that same representations which this process is based. In this way, we analyse, in one side, the globally contrary decoding which subjects made from a conforming code of opposition and, in the other, the structure of feeling which it s based, called structure of feeling of the malaise with politics. Such structure is compound by generating themes which expresses the contraposition about the institutionalized politics and, in the same time, a resignation about politics which fortifies the dominant groups hegemony. We support the thesis which this set of representations about politics is caused by the denial of rights frame which those subjects are immersed

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course