The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

A Contour-based Separation of VerticallyAttached Traffic Signs

This report presents an algorithm for locating the cut points for and separatingvertically attached traffic signs in Sweden. This algorithm provides severaladvanced digital image processing features: binary image which representsvisual object and its complex rectangle background with number one and zerorespectively, improved cross correlation which shows the similarity of 2Dobjects and filters traffic sign candidates, simplified shape decompositionwhich smoothes contour of visual object iteratively in order to reduce whitenoises, flipping point detection which locates black noises candidates, chasmfilling algorithm which eliminates black noises, determines the final cut pointsand separates originally attached traffic signs into individual ones. At each step,the mediate results as well as the efficiency in practice would be presented toshow the advantages and disadvantages of the developed algorithm. Thisreport concentrates on contour-based recognition of Swedish traffic signs. Thegeneral shapes cover upward triangle, downward triangle, circle, rectangle andoctagon. At last, a demonstration program would be presented to show howthe algorithm works in real-time environment.

Concreteness in Business letters : a Corpus-based Analysis of British and Pakistani English

Linguistic features of business letters have been a research target of both linguists and business writers. In this study, the language of British and Pakistani Business letters was compared and contrasted in terms of concreteness and abstractness. A corpus of 100 business letters from Inner Circle and Outer Circle writers were collected for analysis. The findings of the study revealed that British writers use more specific and concrete nouns, definite determiners, numeral, possessive and demonstrative adjectives, cohesive and rhetorical devices than the Pakistani Writers in order to be become concrete and vivid in their communication. The present findings are rather corpus specific since the data include only two countries; however this study may lead to further cross circle research including Expanding Circle research of business letters in terms of concreteness and abstractness. The issue of concreteness in Cross-circle business English can also be studied from psychological, sociological and anthropological perspectives in future Research.

Visualization of spirography-based objective measures in Parkinson's disease

Objective: To investigate whether advanced visualizations of spirography-based objective measures are useful in differentiating drug-related motor dysfunctions between Off and dyskinesia in Parkinson’s disease (PD). Background: During the course of a 3 year longitudinal clinical study, in total 65 patients (43 males and 22 females with mean age of 65) with advanced PD and 10 healthy elderly (HE) subjects (5 males and 5 females with mean age of 61) were assessed. Both patients and HE subjects performed repeated and time-stamped assessments of their objective health indicators using a test battery implemented on a telemetry touch screen handheld computer, in their home environment settings. Among other tasks, the subjects were asked to trace a pre-drawn Archimedes spiral using the dominant hand and repeat the test three times per test occasion. Methods: A web-based framework was developed to enable a visual exploration of relevant spirography-based kinematic features by clinicians so they can in turn evaluate the motor states of the patients i.e. Off and dyskinesia. The system uses different visualization techniques such as time series plots, animation, and interaction and organizes them into different views to aid clinicians in measuring spatial and time-dependent irregularities that could be associated with the motor states. Along with the animation view, the system displays two time series plots for representing drawing speed (blue line) and displacement from ideal trajectory (orange line). The views are coordinated and linked i.e. user interactions in one of the views will be reflected in other views. For instance, when the user points in one of the pixels in the spiral view, the circle size of the underlying pixel increases and a vertical line appears in the time series views to depict the corresponding position. In addition, in order to enable clinicians to observe erratic movements more clearly and thus improve the detection of irregularities, the system displays a color-map which gives an idea of the longevity of the spirography task. Figure 2 shows single randomly selected spirals drawn by a: A) patient who experienced dyskinesias, B) HE subject, and C) patient in Off state. Results: According to a domain expert (DN), the spirals drawn in the Off and dyskinesia motor states are characterized by different spatial and time features. For instance, the spiral shown in Fig. 2A was drawn by a patient who showed symptoms of dyskinesia; the drawing speed was relatively high (cf. blue-colored time series plot and the short timestamp scale in the x axis) and the spatial displacement was high (cf. orange-colored time series plot) associated with smooth deviations as a result of uncontrollable movements. The patient also exhibited low amount of hesitation which could be reflected both in the animation of the spiral as well as time series plots. In contrast, the patient who was in the Off state exhibited different kinematic features, as shown in Fig. 2C. In the case of spirals drawn by a HE subject, there was a great precision during the drawing process as well as unchanging levels of time-dependent features over the test trial, as seen in Fig. 2B. Conclusions: Visualizing spirography-based objective measures enables identification of trends and patterns of drug-related motor dysfunctions at the patient’s individual level. Dynamic access of visualized motor tests may be useful during the evaluation of drug-related complications such as under- and over-medications, providing decision support to clinicians during evaluation of treatment effects as well as improve the quality of life of patients and their caregivers. In future, we plan to evaluate the proposed approach by assessing within- and between-clinician variability in ratings in order to determine its actual usefulness and then use these ratings as target outcomes in supervised machine learning, similarly as it was previously done in the study performed by Memedi et al. (2013).

Dokumentationens dilemman : Förskollärare samtalar om pedagogisk dokumentation

Abstract  Pedagogical documentation is a certain procedure for documenting that, in recent years, has been embraced in several Swedish preschools. Teachers document children’s actions and conversations usually by photos or video recordings. This documentation is to be used for a pedagogical purpose. However, studies and governmental inspections have shown that pedagogical documentation gives rise to many questions among preschool teachers. The purpose of this study is to gain insight into what is being expressed when preschool teachers discuss pedagogical documentation, focusing on themes of content and on the participants’ expressions of their points of view. The data is comprised of transcriptions from audio recordings of discussions conducted in a research circle. The participants are eight preschool teachers that met over the course of one year. Each meeting focused on the documentation provided by a different participant. In that way the contents of the discussions were framed by the teachers own questions and narratives. Theoretically, the study departs from Social Constructionism and Discursive Psychology. The preschool teachers’ utterances have been analyzed using concepts of interpretative repertoires and ideological dilemmas. The results show the main themes to be: Knowledge content in a preschool setting, children’s learning, the teacher’s role and implementation of pedagogical documentation. The participants’ joint position is that the knowledge content at the preschool level is defined by the curriculum for the preschool. Concerning children’s learning and the teacher’s role, two main standpoints are disclosed. Ideologically those standpoints derive from two opposing theories of education. Based on how the standpoints have been expressed I have called them ”predetermined learning” versus ”non-predetermined learning”. One main distinction between the standpoints is that predetermined learning emphasizes the results of learning, while non-predetermined learning emphasizes the processes of learning. The participants’ utterances show that teachers tend to subscribe to the idea that there is only one acceptable way of working with pedagogical documentation. This sometimes creates performance anxiety and feelings of not succeeding and has led to arguments advocating an alternate approach; pedagogical documentation can be done in many ways. The ideological dilemmas within the discourse can be perceived as resources by which the participants argue about knowledge, learning, teaching and about the implementation of pedagogical documentation.

Capability outcomes from educational and ICT capability inputs : an analysis of ICT use in informal education in Kenya

In the field of Information and Communication Technologies for Development (ICT4D) ICT use in education is well studied. Education is often seen as a pre-requisite for development and ICTs are believed to aid in education, e.g. to make it more accessible and to increase its quality. In this paper we study the access and use of ICT in a study circle (SC) education program in the south coast of Kenya. The study is qualitative reporting results based on interviews and observations with SC participants, government officers and SC coordinators and teachers. The study builds on the capability approach perspective of development where individuals’ opportunities and ability to live a life that they value are focused. The aim of the study is to investigate the capability outcomes enabled through the capability inputs access and use of ICT in education as well as the factors that enabled and/or restricted the outcomes. Findings show that many opportunities have been enabled such as an increase in the ability to generate an income, learning benefits, community development and basic human development (e.g. literacy and self-confidence). However, conversion factors such as a poorly developed infrastructure and poor IT literacy prevent many of the individuals from taking full advantage of the ICT and the opportunities it enables. 

The Carbon Emissions of the Boston Red Sox

The Boston Red Sox emit a great deal of carbon throughout the regular baseball season because of flights to the home fields of their opponents. Knowing that air travel is one of the biggest transportation-based contributors to global climate change, the Boston Red Sox (and all major league teams) should be encouraged to offset their carbon emissions from regular season travel. Using ArcGIS to map the flight paths along great circle routes, the distance of flights to opponents’ cities was calculated to total the number of miles traveled in the 2008 season. The price of offsetting this carbon was estimated using the calculators of carbon offset retailers, such as Native Energy, a Vermont-based retailer. This project provides the potential costs of offsetting the carbon emitted from Red Sox air travel. To take the lead in the future of the Northeast, the Red Sox should begin to consider their contribution to climate change.

Contrato de Gestão: A Experiência da CESAN

o objetivo deste estudo é explorar os motivos que levaram à interrupção do contrato de gestão da CESAN, sem uma explicação relevante. A análise da crise gerada com o fracasso do contrato de gestão da CESAN, considerado naquele período de gestão como ferramenta indispensável ao apoio gerencial, demonstrou a necessidade de aprofundar conhecimento sobre o assunto. Estudos foram realizados buscando uma explicação, particularmente no que se refere à verificação do grau de integração dos sistemas de planejamento da CESAN e o Estado, assim como o comprometimento político e a consistência do arcabouço institucional do contrato. O produto da pesquisa foi apresentado a profissionais da CESAN devidamente qualificados, com formação acadêmica em Mestrado e/ou MBA, que, após sua leitura, participaram de rodadas de conhecimento e reuniões críticas, com a finalidade de tornar o conteúdo do documento mais completo e próximo da realidade vivenciada. O conhecimento gerado dará contribuições de alta relevãncia para o setor, uma vez que os três níveis de governo carecem de ferramentas semelhantes ao contrato de gestão como estratégia para reverter a incapacidade da máquina pública. As experiências encontradas em documentações e no meio literário aqui reunidas, permitiram avaliar a objetividade de critérios e o nível de comprometimento entre os diversos segmentos envolvidos, condições básicas para a sustentação e a continuidade do contrato de gestão.

Sistema de gestão de unidade judicial

A prestação jurisdicional eficiente e eficaz é uma exigência social e constitucional. Um círculo virtuoso pode ser instaurado pela cobrança social de melhoria dos serviços prestados pelo Poder Judiciário. A resposta a essa exigência é necessária, com a reformulação e revisão de conceitos, estruturas e cultura organizacional. A atuação nessa seara impacta a legitimação do Poder Judiciário, podendo elevá-la tanto mais satisfeitas as expectativas sociais. Os conceitos de gestão e sua implementação devem ser parte das atividades judiciais, desde a alta administração até a gestão da unidade judicial. Há necessidade, portanto, de um sistema de gestão que permeie todas as atividades desenvolvidas. O Tribunal de Justiça do Rio Grande do Sul desde 1995 adotou o Programa Gaúcho de Qualidade e Produtividade (PGQP), através do Plano de Gestão pela Qualidade no Poder Judiciário do Rio Grande do Sul (PGQJ). A recente formulação do Planejamento Estratégico trouxe novas perspectivas, objetivos e desafios. A concreção dos objetivos estratégicos traçados depende do alinhamento das unidades judiciais. Surge aí a importância de um sistema de gestão das unidades judiciais, com elementos e indicadores definidos, permitindo a visualização pela alta administração do andamento da instituição em busca dos objetivos estabelecidos. Alinhada à importância do tema, propõe-se a apresentação dos principais elementos formadores de um sistema de gestão de unidade judicial: direcionamento e alinhamento estratégico; planejamento da microgestão; estrutura organizacional; processos de trabalho; procedimentos operacionais padrão; rotinas cartorárias; gestão de pessoas; treinamento e liderança. O Sistema de Gerenciamento Matricial dos Serviços Judiciários (GMS- JUD), desenvolvido pelo Tribunal de Justiça do Rio Grande do Sul com a consultoria do Instituto Nacional de Desenvolvimento Gerencial (INDG), é apresentado como direcionador de acompanhamento do planejamento traçado pelas unidades judiciais, compondo o sistema de gestão proposto.

Implantação de sistema de gestão na vara da infância e juventude de Porto Velho

Crianças e adolescentes necessitam de proteção integral e prioridade na implementação de seus direitos fundamentais individuais. A demora na tramitação dos processos judiciais constitui um grave problema da Justiça. A eficiência do Poder Judiciário em distribuir justiça está condicionada à prestação jurisdicional rápida, à efetividade do processo. As transformações sociais, econômicas, tecnológicas têm operado muitas mudanças na rotina dos Tribunais. Uma delas é a implantação do sistema de gestão da qualidade nas serventias judiciais. A qualidade da prestação jurisdicional dependerá da gestão imprimida pelo juiz na sua unidade. Diante disso, o presente trabalho destina-se a apresentar uma proposta de sistema de gestão no âmbito da Vara da Infância e Juventude de Porto Velho, Estado de Rondônia, dividido em catorze etapas: foco da organização, direcionadores estratégicos, planejamento da gestão, estrutura organizacional, comunicação, gestão de pessoas, infraestrutura, processos de trabalho, documentos e normas, registros, medição, tratamento de falhas, análise crítica e avaliação dos resultados.

Entre um cafezinho e uma bica: uma análise do uso do café por consumidores cariocas e alfacinhas

O estudo do comportamento dos consumidores  nomeadamente, os rituais de consumo associados ao consumo de café e os fatores envolvidos nesse processo  é importante para podermos compreender e comparar o comportamento dos consumidores cariocas e lisboetas no que tange ao consumo de café. Por outro lado, também é importante averiguar a influência da cultura e da sociedade nesses rituais de consumo, de forma a compreender a evolução do varejo de café pronto no Brasil. Os modelos que vêm sendo aplicados aqui se adaptam às características do público local, o que traz para a nossa discussão, a noção de cultura. Como em Portugal o uso do café expresso já é mais maduro que no Rio de Janeiro, a comparação entre as duas culturas pode ser interessante para ajudar o varejo brasileiro a se desenvolver. Para tal, neste estudo, foram entrevistados moradores das cidades do Rio de Janeiro e de Lisboa, a fim de descrevermos de que modo consomem café, os rituais associados a esse bem de consumo, assim como seus hábitos, motivações e justificativas para esse consumo, mostrando que não trata apenas de uma decisão de compra utilitária, mas também simbólica. Com esse objetivo, foram entrevistadas 69 e pessoas e os resultados dessas entrevistas avaliados de forma interpretativa. A conclusão foi a de que a bebida é consumida por uma parcela heterogênea dos entrevistados e que, geralmente, os consumidores associam o consumo de café a hábito, prazer, círculo de amizades, trabalho – como break –, colegas e família. Isso revela que o significado social da bebida está enraizado no âmbito doméstico, no trabalho ou no círculo de amizades e que esse significado está intrinsecamente associado aos hábitos e costumes das sociedades brasileira e portuguesa como fruto de suas culturas. Consequentemente, grande parte dos rituais de consumo dessa bebida está interligada ao seu significado social. Observou-se a necessidade de expansão desse mercado, particularmente, entre os jovens no Rio de Janeiro, e que muitas vezes o aroma é preferível ao sabor, pois mesmo aqueles que não apreciam muito a bebida, de uma forma geral, afirmaram gostar bastante do aroma. Assim, é fundamental para os gestores de estabelecimentos de varejo de café pronto conhecerem o cliente, serem inovadores e anteciparem as tendências, de modo a satisfazerem as necessidades deste. A preocupação não deve ser apenas com a qualidade do produto oferecido e com o conforto do cliente, mas também em agregar valor ao café e ao serviço prestado, proporcionando à clientela uma experiência única, a qual pode ser um diferencial importante, pois a conotação simbólica associada a esse bem de consumo é cada vez mais destacada.