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.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Formation of out of plane oxime metallacycles in [Cu(2)] and [Cu(4)] complexes

The reaction Of Cu(ClO(4))(2)center dot 6H(2)O with dimethylglyoxime (H(2)dmg) in a 1:1 mole ratio in aqueous methanol at room temperature affords the dinuclear complex [Cu(2)(mu-Hdmg)(4)] (1). Reaction of 1 with [Cu(bpy)(H(2)O)(2)](ClO(4))(2) (bpy = 2,2`-bipyridine) in a 1:1 mole ratio in aqueous methanol at room temperature yields the tetranuclear complex [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](ClO(4))(2) (2). The direct reaction of Cu(ClO(4))(2)center dot 6H(2)O with H(2)dmg and bpy in a 2:21 mole ratio in aqueous methanol at room temperature also yields 2 quantitatively. The complexes 1 and 2 were structurally characterized by X-ray crystallography. Unlike the binding in Ni/Co-dmg, two different types of N-O bridging modes during the oxime based metallacycle formation and stacking of square planar units have been identified in these complexes. The neutral dinuclear complex 1 has CuN(4)O coordination spheres and complex 2 consists of a dicationic [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](2+) unit and two uncoordinated ClO(4)(-) anions having CuN(4)O and CuN(2)O(3) coordination spheres. The two copper(II) ions are at a distance of 3.846(8) angstrom in 1 for the trans out of plane link and at 3.419(10) and 3.684(10) angstrom in 2 for the trans out of plane and cis in plane arrangements, respectively. The average Cu-N(oxime) distances are 1.953 and 1.935 angstrom, respectively. The average basal and apical Cu-N(oxime) distances are 1.945, 2.295 and 2.429 angstrom. The UV-Vis spectra of 2 is similar to the spectrum of the reaction mixture of 1 and [Cu(bpy)(H(2)O)(2)](2+). Variable temperature magnetic properties measurement shows that the interaction between the paramagnetic copper centers in complex I is antiferromagnetic in nature. The EPR spectra of frozen solution of the complexes at 77 K consist of axially symmetric fine-structure transitions (Delta M(S) = 1) and half-field signals (Delta M(S) = 2) at ca. 1600 G, suggesting the presence of appreciable Cu-Cu interactions. (C) 2009 Elsevier Ltd. All rights reserved.

Padronização de um método para mensuração das tábuas ósseas vestibular e lingual dos maxilares na Tomografia Computadorizada de Feixe Cônico (Cone Beam)

INTRODUÇÃO: a espessura das tábuas ósseas que recobrem os dentes por vestibular e lingual constitui um dos fatores limitantes da movimentação dentária. O avanço tecnológico em Imaginologia permitiu avaliar detalhadamente essas regiões anatômicas por meio da utilização da tomografia computadorizada de feixe cônico (TCFC). OBJETIVO: descrever e padronizar, pormenorizadamente, um método para mensuração das tábuas ósseas vestibular e lingual dos maxilares nas imagens de tomografia computadorizada de feixe cônico. METODOLOGIA: a padronização digital da posição da imagem da face deve constituir o primeiro passo antes da seleção dos cortes de TCFC. Dois cortes axiais de cada maxilar foram empregados para a mensuração da espessura do osso alveolar vestibular e lingual. Utilizou-se como referência a junção cemento-esmalte dos primeiros molares permanentes, tanto na arcada superior quanto na inferior. RESULTADOS: cortes axiais paralelos ao plano palatino foram indicados para avaliação quantitativa do osso alveolar na maxila. Na arcada inferior, os cortes axiais devem ser paralelos ao plano oclusal funcional. CONCLUSÃO: o método descrito apresenta reprodutibilidade para utilização em pesquisas, assim como para a avaliação clínica das repercussões periodontais da movimentação dentária, ao permitir a comparação de imagens pré e pós-tratamento.

Influência do estreitamento do canal vertebral e do tempo para a descompressão na recuperação locomotora de ratos

OBJETIVO: o objetivo deste trabalho foi estudar as consequências da lesão por contusão da medula espinhal, associada ao estreitamento do canal vertebral, no comportamento motor de ratos, avaliando-se o efeito do tempo para descompressão na recuperação neurológica dos animais. MÉTODOS: foram utilizados ratos Wistar machos (n=6 por grupo), subdivididos nos seguintes grupos experimentais: laminectomia (T9-T10, Grupo Controle), contusão por queda de peso (10 g de peso, 15 cm de altura), estreitamento do canal vertebral em 35% (hastes de policarbonato; espessura de 0,78 mm) e contusão associada ao estreitamento do canal vertebral. O grupo de lesão associada foi ainda subdividido em sem ou com descompressão 24 ou 72 horas após a cirurgia. Os animais foram sacrificados sete dias após os procedimentos cirúrgicos. A função locomotora dos animais foi avaliada por meio do teste do campo aberto, do teste do plano inclinado e pela aplicação da escala BBB, antes da cirurgia, 24 e 72 horas depois da cirurgia e após 7 dias do procedimento cirúrgico. RESULTADOS: a lesão por queda de peso e compressão da medula espinhal, bem como a lesão mista, prejudicaram o comportamento motor dos animais, sendo que a descompressão cirúrgica após 24 e 72 horas da cirurgia não melhorou a recuperação motora dos animais, como mostram os resultados da avaliação de campo aberto, no plano inclinado e pela escala BBB. Por outro lado, os animais que sofreram lesão medular por queda de peso apresentaram melhores escores na escala BBB e ângulos maiores no plano inclinado do que aqueles que sofreram lesão por estreitamento do canal vertebral ou lesão mista. CONCLUSÕES: a lesão por queda de peso ou estreitamento do canal vertebral provocou alterações no comportamento motor dos animais, sendo que a descompressão não trouxe melhora funcional significativa.

Evaluation of simulated bone lesion in the head of the mandible by using multislice computed tomography

Conventional radiography has shown limitation in acquiring image of the ATM region, thus, computed tomography (CT) scanning has been the best option to the present date for diagnosis, surgical planning and treatment of bone lesions, owing to its specific properties. OBJECTIVE: The aim of the study was to evaluate images of simulated bone lesions at the head of the mandible by multislice CT. MATERIAL AND METHODS: Spherical lesions were made with dental spherical drills (sizes 1, 3, and 6) and were evaluated by using multislice CT (64 rows), by two observers in two different occasions, deploying two protocols: axial, coronal, and sagittal images, and parasagittal images for pole visualization (anterior, lateral, posterior, medial and superior). Acquired images were then compared with those lesions in the dry mandible (gold standard) to evaluate the specificity and sensibility of both protocols. Statistical methods included: Kappa statistics, validity test and chi-square test. Results demonstrated the advantage of associating axial, coronal, and sagittal slices with parasagittal slices for lesion detection at the head of the mandible. RESULTS: There was no statistically significant difference between the types of protocols regarding a particular localization of lesions at the poles. CONCLUSIONS: Protocols for the assessment of the head of the mandible were established to improve the visualization of alterations of each of the poles of the mandible's head. The anterior and posterior poles were better visualized in lateral-medial planes while lateral, medial and superior poles were better visualized in the anterior-posterior plane.

Influência da proporção entre as alturas do ramo mandibular e dentoalveolar posterior na inclinação do plano mandibular

OBJETIVO: avaliar a existência de correlação entre a proporção da altura do ramo mandibular (AR) com a altura dentoalveolar posterior total (ADAPT) e a inclinação do plano mandibular (PM). MÉTODOS: dois examinadores avaliaram 81 telerradiografias laterais de pacientes, com idades a partir de 18 anos, do arquivo do curso de especialização em Ortodontia e Ortopedia Facial da Faculdade de Odontologia da UFBA. As radiografias foram digitalizadas, os pontos marcados e as medidas obtidas através do programa Radiocef 1.0. Mediu-se a inclinação do plano mandibular para caracterizar o padrão vertical da face e dividir as radiografias em três grupos: grupo de face normal (GN), de 22º a 28º, de face curta (GC), menor que 22º, e de face longa (GL), maior que 28º. A inclinação do plano palatino serviu como critério de exclusão, sendo que valores abaixo de -2,5° ou acima de 3,5º foram excluídos. Desta forma, 46 telerradiografias laterais totalizaram a amostra. RESULTADOS: a AR diferiu entre GC e GL, porém não houve diferença estatisticamente significante para as alturas dentoalveolares posteriores. Houve baixa correlação entre a AR e a ADAPT nos grupos, no entanto, a correlação da proporção entre essas alturas com a inclinação do PM mostrou-se estatisticamente significante e negativa. CONCLUSÃO: este é um fator a ser levado em consideração na avaliação do PM, quando do diagnóstico e tratamento das displasias verticais dentofaciais.

Atividade óptica de um meio dielétrico diluído: Pasteur e as simetrias moleculares

Em 1848 Pasteur conjeturou que a rotação do plano de polarização da luz em um meio diluído é gerada pelas propriedades de simetria das moléculas do meio no qual a luz se propaga. O objetivo do nosso artigo é de mostrar que Pasteur estava correto usando conhecimentos de eletromagnetismo e mecânica quântica de um curso de graduação em física. Faremos um breve retrospecto das ideias básicas da teoria eletromagnética necessárias para o estudo da atividade óptica. A seguir, usando a teoria de perturbações em mecânica quântica e levando em conta as simetrias das moléculas calcularemos a atividade óptica do meio. Mostraremos que as previsões teóricas, que estão plenamente de acordo com os resultados experimentais, comprovam a hipótese de Pasteur.

Distribuição de tensões em mini-implantes ortodônticos

O objetivo deste trabalho foi avaliar a distribuição de tensões na resina em contato com os filetes de roscas de mini-implantes cilíndricos e cônicos, submetidos à carga lateral e torção de inserção. Um modelo fotoelástico foi confeccionado com gelatina transparente, para simular o osso alveolar. O modelo foi observado com um polariscópio plano e fotografado antes e após a ativação dos mini-implantes com força lateral e de inserção. A aplicação de cargas laterais provocou momentos fletores nos mini-implantes, aparecimento de franjas isocromáticas ao longo dos filetes do corpo dos mini-implantes e no ápice. Quando foi aplicado o torque de inserção, verificou-se a concentração de tensões próxima ao ápice. Concluiu-se que: (1) o mini-implante cilíndrico apresentou maior concentração de tensões no ápice, e (2) o mini-implante cônico apresentou maior concentração de tensões nos filetes de rosca apicais.

Revised criteria for the assessment and interpretation of occlusal deviations in the deciduous dentition: a public health perspective

Dados secundários de uma amostra aleatória de pré-escolares brasileiros foram analisados com o objetivo de avaliar a prevalência de desvios oclusais na dentição decídua, que podem adversamente afetar a dentição permanente, com base em critérios revisados. Overjet e overbite apresentaram pontos de corte descritos na literatura para a remoção dos casos de má oclusão leve. Overjet > 3mm e overbite > 3mm afetaram 16% e 7% das crianças, respectivamente. No plano sagital foram consideradas apenas as taxas de desvios bilaterais: relação molar em degrau distal (9,7%) e mesial (6,0%); relação dos caninos Classe 2 (11,0%) e Classe 3 (2,9%). Para os demais desvios não foram relatados na literatura critérios de severidade. Valores brutos de mordida aberta anterior (27,9%); mordida cruzada posterior (11,3%); apinhamento dentário maxilar (7,0%) e mandibular (11,3%) foram registrados. A avaliação da má oclusão na dentição decídua deve considerar a severidade dos desvios para a identificação de casos e não-casos de relevância em saúde pública. Enfatiza-se a necessidade de maior consenso e melhora na interpretação de dados epidemiológicos sobre a má oclusão nesse estágio de desenvolvimento

Evaluation of Femtosecond Laser-Induced Breakdown Spectroscopy for Analysis of Animal Tissues

The aim of this work was to evaluate the performance of femtosecond laser-induced breakdown spectroscopy (fs-LIBS) for the determination of elements in animal tissues. Sample pellets were prepared from certified reference materials, such as liver, kidney, muscle, hepatopancreas, and oyster, after cryogenic grinding assisted homogenization. Individual samples were placed in a two-axis computer-controlled translation stage that moved in the plane orthogonal to a beam originating from a Ti:Sapphire chirped-pulse amplification (CPA) laser system operating at 800 mu and producing a train of 840 mu J and 40 fs pulses at 90 Hz. The plasma emission was coupled into the optical fiber of a high-resolution intensified charge-coupled device (ICCD)-echelle spectrometer. Time-resolved characteristics of the laser-produced plasmas showed that the best results were obtained with delay times between 80 and 120 ns. Data obtained indicate both that it is a matrix-independent sampling process and that fs-LIBS can be used for the determination of Ca, Cu, Fe, K, Mg, Na, and P, but efforts must be made to obtain more appropriate detection limits for Al, Sr, and Zn.

Relationship Between Eccentric Hip Torque and Lower-Limb Kinematics: Gender Differences

The purposes of this study were to compare lower-limb kinematics between genders, and determine the relationships among eccentric hip abductor and lateral rotator torques and lower-limb kinematics. The movements of the pelvis, femur, and knee were calculated for 16 women and 16 men during the single-leg squat. Eccentric hip abductor and lateral rotator torques were measured using an isokinetic dynamometer. The results showed that women had greater contralateral pelvic depression, femur adduction, and knee abduction than men. The eccentric hip abductor and lateral rotator torques were correlated with coronal plane femur and knee movements in the overall sample. When the genders were analyzed separately, it was observed that women with greater eccentric hip abductor torque exhibited less femur adduction and femur medial rotation, and greater knee adduction excursion. No significant relationship was observed between the isokinetic and kinematic variables in the male group. The differences between the genders help to explain the greater rate of knee disorders observed in women. Moreover, the eccentric hip abduction action seemed to be more important in women to control the lower-limb movements.

Gait kinematic analysis in patients with a mild form of central cord syndrome

Background: Central cord syndrome (CCS) is considered the most common incomplete spinal cord injury (SCI). Independent ambulation was achieved in 87-97% in young patients with CCS but no gait analysis studies have been reported before in such pathology. The aim of this study was to analyze the gait characteristics of subjects with CCS and to compare the findings with a healthy age, sex and anthropomorphically matched control group (CG), walking both at a self-selected speed and at the same speed. Methods: Twelve CCS patients and a CG of twenty subjects were analyzed. Kinematic data were obtained using a three-dimensional motion analysis system with two scanner units. The CG were asked to walk at two different speeds, at a self-selected speed and at a slower one, similar to the mean gait speed previously registered in the CCS patient group. Temporal, spatial variables and kinematic variables (maximum and minimum lower limb joint angles throughout the gait cycle in each plane, along with the gait cycle instants of occurrence and the joint range of motion ROM) were compared between the two groups walking at similar speeds. Results: The kinematic parameters were compared when both groups walked at a similar speed, given that there was a significant difference in the self-selected speeds (p < 0.05). Hip abduction and knee flexion at initial contact, as well as minimal knee flexion at stance, were larger in the CCS group (p < 0.05). However, the range of knee and ankle motion in the sagittal plane was greater in the CG group (p < 0.05). The maximal ankle plantar-flexion values in stance phase and at toe off were larger in the CG (p < 0.05). Conclusions: The gait pattern of CCS patients showed a decrease of knee and ankle sagittal ROM during level walking and an increase in hip abduction to increase base of support. The findings of this study help to improve the understanding how CCS affects gait changes in the lower limbs.

Power Secant Method applied to natural frequency extraction of Timoshenko beam structures

This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named ""power deflation"", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

A simple procedure for reliability assessment of thin composite plates against buckling

In some circumstances ice floes may be modeled as beams. In general this modeling supposes constant thickness, which contradicts field observations. Action of currents, wind and the sequence of contacts, causes thickness to vary. Here this effect is taken into consideration on the modeling of the behavior of ice hitting inclined walls of offshore platforms. For this purpose, the boundary value problem is first equated. The set of equations so obtained is then transformed into a system of equations, that is then solved numerically. For this sake an implicit solution is developed, using a shooting method, with the accompanying Jacobian. In-plane coupling and the dependency of the boundary terms on deformation, make the problem non-linear and the development particular. Deformation and internal resultants are then computed for harmonic forms of beam profile. Forms of giving some additional generality to the problem are discussed.