On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Unlinked Embedded Graphs

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one that contains only trivial knots or links. Examples show that the invariant is sufficiently powerful to distinguish some different unlinked embeddings of the same graph.

Avaliação cefalométrica das alterações dentoesqueléticas de jovens com má oclusão de Classe II dentária tratados com distalizadores Jones jig

OBJETIVO: esta pesquisa objetivou avaliar cefalometricamente as alterações dentoesqueléticas de jovens com Classe II dentária tratados com o distalizador Jones jig. METODOLOGIA: foram avaliados 30 pacientes, sendo 15 de cada gênero, com média de idades iniciais de 13,63 anos; brasileiros, naturais da cidade de Bauru/SP, caracterizados por má oclusão de Classe II, 1ª e 2ª divisões de Angle sem comprometimento esquelético. Os jovens foram tratados com aparelho Jones jig a fim de distalizar os molares superiores a uma relação molar de "super Classe I"; sendo que esse dispositivo permaneceu, em média, por 0,55 anos. Ao final da sobrecorreção, os molares distalizados receberam um botão de Nance e, como ancoragem extrabucal, o aparelho extrabucal (AEB) com tração média-alta, com o intuito de verticalizar e corrigir a angulação radicular dos molares distalizados. Foram realizadas telerradiografias em normal lateral inicial (T1) e pós-distalização (T2). As medidas cefalométricas foram submetidas ao teste t dependente de Student para avaliar as alterações de T1 para T2. RESULTADOS: com base nos resultados obtidos e a partir da metodologia empregada, observou-se alterações dentárias significativas, como a movimentação distal linear e angular, assim como a intrusão dos segundos e primeiros molares superiores no sentido vertical. Também se confirmou efeitos indesejáveis, como a perda de ancoragem refletida em mesialização, extrusão e angulação mesial dos segundos pré-molares, a protrusão dos incisivos superiores e o aumento do trespasse vertical e horizontal. Pode-se confirmar que certas movimentações dentárias promovem significativas alterações esqueléticas de estruturas localizadas à distância, ou seja, observou-se extrusão significativa dos segundos pré-molares superiores, o que resultou em rotação mandibular, aumento significativo da altura facial anteroinferior e protrusão do lábio inferior. CONCLUSÃO: pode-se concluir que o distalizador Jones jig promove, basicamente, alterações dentárias.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Claude Jones addressing a Communist Party of Australia meeting in Brisbane, Australia

Claude Jones addressing a Communist Party of Australia meeting in Brisbane, Australia. Ted Bacon can be seen at the table.

Changes in quantum efficiency of Photosystem II of symbiotic dinoflagellates of corals after heat stress, and of bleached corals sampled after the 1998 Great Barrier Reef mass bleaching event Ross J. Jones , Selina Ward, Affendi Yang Amri and Ove Hoegh-Guldberg

Pulse-amplitude-modulation chlorophyll fluorometry was used to examine changes in dark-adapted F-v/F-m of endosymbiotic dinoflagellate microalgae within the tissues of the temperate coral Plesiastrea versipora exposed to elevated seawater temperature. The F-v/F-m was markedly reduced following exposure of corals to 28 degrees C for 48 h. When corals were returned to ambient (24 degrees C) conditions, F-v/F-m increased in an initial rapid and then secondary slower phase. Tissue discolouration (coral bleaching), caused by a significant decrease in the density of algae, was observed during the first 2-3 days of the recovery period. After 14 days, F-v/F-m was still significantly lower than in control corals. The recovery of F-v/F-m is discussed in terms of repair processes within the symbiotic algae, division of healthy algae and also the selective removal of photo-damaged dinoflagellates. Under field conditions, bleached corals sampled at Heron Island Reef during a bleaching event had significantly lower F-v/F-m than non-bleached colonies; four months after the bleaching event, there were no differences in F-v/F-m or algal density in corals marked as having bleached or having shown no signs of colour loss. The results of this laboratory and field study are consistent with the hypothesis that an impairment of photosynthesis occurs during heat-stress, and is the underlying cause of coral bleaching.

Comparative distalization effects of Jones jig and pendulum appliances

Introduction: In this study, we compared the dentoalveolar changes of Class II patients treated with Jones jig and pendulum appliances. Methods: The experimental group comprised 40 Class II malocclusion subjects, divided into 2 groups: group 1 consisted of 20 patients (11 boys, 9 girls) at a mean pretreatment age of 13.17 years, treated with the Jones jig appliance for 0.91 years; group 2 comprised 20 patients (8 boys, 12 grls) at a mean pretreatment age of 13.98 years, treated with the pendulum appliance for 1.18 years. Only active treatment time of molar distalization was evaluated in the predistalization and postdistalization lateral cephalograms. Molar, second premolar, and incisor angular and linear variables were obtained. The intergroup treatment changes in these variables were compared with independent t tests. Results: The maxillary second premolars showed greater mesial tipping and extrusion in the Jones jig group, indicating more anchorage loss during molar distalization with this appliance. The amounts and the monthly rates of molar distalization were similar in both groups. Conclusions: The Jones jig group showed greater mesial tipping and extrusion of the maxillary second premolars. The mean amounts and the monthly rates of first molar distalization were similar in both groups. (Am J Orthod Dentofacial Orthop 2009;135:336-42)

O efeito da técnica de inibição de Jones nos músculos Masseter e temporal nas disfunções temporomandibulares

Introdução: A disfunção temporomandibular (DTM), de causa muscular, caracteriza-se por uma dor músculo-esquelética crónica, com sinais e sintomas específicos como a presença de Trigger Points (TrPs). Objetivo: Avaliar o efeito da Técnica de Inibição de Jones (TIJ) nos músculos masseter e temporal em indivíduos com DTM, e a identificação dos sinais e sintomas, a relação entre a severidade da DTM, a ansiedade e a qualidade de sono. Métodos: Estudo quasi-experimental, constituído por 16 indivíduos no grupo experimental (GE) e 17 grupo controle (GC). O grau de severidade foi avaliado pelo Índice de Helkimo e as alterações do sono pelo questionário de Pittsburgh sobre a qualidade do sono. Apenas o GE foi sujeito a uma TIJ nos TrPs latentes dos músculos masseter e temporal. Os dois grupos foram avaliados pré-intervenção (M0), pós-intervenção (M1) e 3 semanas após (M2), as amplitudes de movimento ativas de abertura, lateralidade direita/esquerda e protusão da boca bem como a dor (EVA) em repouso e na abertura máxima. Resultados: Foi possível observar que quanto maior o grau de DTM, maior a frequência de ansiedade e pior a qualidade do sono. Observou-se um decréscimo de TrPs, no GE, após a aplicação da técnica, principalmente no masseter. Não foi possível verificar diferenças inter-grupos. Contudo, observou-se no GE uma melhoria em todas as amplitudes avaliadas entre o M0 e o M2. Em relação à EVA em repouso e na abertura máxima, o GE demonstrou diminuição da dor no M1 e manteve valores inferiores no M2. Conclusão: Verifica-se uma diminuição dos TrPs, uma melhoria das amplitudes ativas bem como uma diminuição da dor após a aplicação da TIJ no GE. Já ao longo do tempo, o efeito é menos expressivo contudo observam-se valores inferiores comparativamente a M0.

Dynamics of the Dow Jones and the NASDAQ stock indexes

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.