Lie Groups and mechanics: an introduction

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm equation

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.Comment: 13 pages, 6 figure

Knowledge, self-efficacy and behavioural intent towards AIDS prevention behaviours among culturally diverse secondary school pupils in South Africa

Objective: To investigate knowledge, self-efficacy, and behavioural intent towards AIDS prevention behaviours among culturally diverse secondary school pupils in South Africa.Design: Randomised study.Setting: Three urban secondary schools in Pietersburg, South Africa.Participants: Three hundred and sixty six Grade 11 secondary school pupils, comprising 150 (41%) males, and 216 (59%) females, aged 17 to 24 years (mean age 19.3 years, SD=2.6). The three cultural groups were 142 Blacks, 112 Whites and 112 Asians. Main outcome measures: The questionnaire included items on socio-economic and family background, knowledge about HIV, perceived self-efficacy and behavioural intent regarding AIDS preventive behaviours.Results: Overall, the participants showed an adequate level of AIDS knowledge. However, there was considerable inaccuracy regarding AIDS transmission myths or how AIDS cannot be transmitted. The different cultural groups generally felt most self- efficacious regardinghow to protect themselves from becoming infected (75-90%) and least self-efficacious on knowing where to go for information on AIDS (72-74%). Generally, participants reported a high behavioural intent. The Whites stand second in knowledge and more or less second inself-efficacy and behaviour intent. The Blacks stand third in knowledge and more or less second in self-efficacy and behaviour intent.Conclusion: Culturally diverse knowledge, self-efficacy and behavioural intent towards AIDS prevention was found among White, Black and Asian pupils, which should inform a culturally sensitive and appropriate AIDS health promotion programme in South Africa

Nonholonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 200

Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Assessment of RNAi-induced silencing in banana (Musa spp.)

In plants, RNA- based gene silencing mediated by small RNAs functions at the transcriptional or post-transcriptional level to negatively regulate target genes, repetitive sequences, viral RNAs and/or transposon elements. Post-transcriptional gene silencing (PTGS) or the RNA interference (RNAi) approach has been achieved in a wide range of plant species for inhibiting the expression of target genes by generating double-stranded RNA (dsRNA). However, to our knowledge, successful RNAi-application to knock-down endogenous genes has not been reported in the important staple food crop banana

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

Classical Signal Model for Quantum Channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. In this note we consider some consequences of PCSFT for quantum information theory. They are based on the observation \cite{W} of two authors of this paper that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transformations of classical Gaussian signa