Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group

This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity. The acceleration and angular velocity can be chosen either aligned or perpendicular, and in the latter case the angular velocity can be chosen equal or smaller than than the acceleration. We start reviewing the classical Euler's and Chasles' theorems both in the Lie algebra and group versions. We recall the relativistic generalization of Euler's theorem and observe that every (infinitesimal) transformation can be recovered from information of algebraic and geometric type, the former being identified with the conjugacy class and the latter with some additional geometric ingredients (the screw axis in the usual non-relativistic version). Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in detail. We prove its exponentiality and identify a causal semigroup and the corresponding Lie cone. Through the identification of new Ad-invariants we classify the conjugacy classes, and show that those which admit a causal representative have special physical significance. These results imply a classification of the inequivalent Killing vector fields of Minkowski spacetime which we express through simple representatives. Finally, we arrive at the mentioned generalization of Chasles' theorem.Comment: Latex2e, 49 pages. v2: few typos correcte

Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

Future asymptotic expansions of Bianchi VIII vacuum metrics

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces correcte

Realizations of Causal Manifolds by Quantum Fields

Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the homogenous spaces \D(n)=\GL(\C^n_\R)/\U(n) with $n=1$ for mechanics and $n=2$ for relativistic fields. The rank $n$ gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e. two characteristic masses in the relativistic case. 'Canonical' field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifold \D(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable - in addition to representations with eigenvectors (states, particle) they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field.Comment: 36 pages, latex, macros include

A holomorphic representation of the Jacobi algebra

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references update

Financial capability and functional financial literacy in young adults with developmental language disorder

Background: Financial capability is an essential feature of the organisation of one’s personal life and engagement with society. Very little is known of how adequately individuals with developmental language disorder (DLD) handle financial matters. It is known that language difficulties place them at a disadvantage in many aspects of their development and during their transition into adulthood, leading to the possibility that financial issues may prove burdensome for them. This study examines the financial capability and functional financial literacy of young adults with DLD and compares them to those of age matched peers (AMPs). We tested the expectation that those with DLD would find financial management more challenging than would their peers, and that they would need to seek greater support from family members or other people. Methods: Participants completed a detailed individual interview, which included items drawn from the British Household Panel Survey and additional measures of financial capability, functional financial literacy and of perceived support. Nonverbal IQ, language, reading and numeracy measures were also collected. Results: Compared to typically developing AMPs, young people with DLD report less extensive engagement with financial products and lower competence in functional financial literacy. A considerably higher proportion of those with DLD (48% vs 16% of AMPs) report that they draw on support, primarily from parents, in various financial tasks, including paying bills, choosing financial products, and taking loans from family or friends. Conclusions: This is the first study to consider the financial capability skills and functional financial literacy of young adults with DLD. We provide novel evidence that some young adults with DLD lack functional financial skills and require support to successfully manage their finances. This has policy implications that relate not only to engaging affected individuals in discussions about financial management but also to wider familial support

Causal structures and causal boundaries

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.Comment: Final version. To appear in Classical and Quantum Gravit

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

High-throughput synthesis of CeO₂ nanoparticles for transparent nanocomposites repelling Pseudomonas aeruginosa biofilms

Preventing bacteria from adhering to material surfaces is an important technical problem and a major cause of infection. One of nature’s defense strategies against bacterial colonization is based on the biohalogenation of signal substances that interfere with bacterial communication. Biohalogenation is catalyzed by haloperoxidases, a class of metal-dependent enzymes whose activity can be mimicked by ceria nanoparticles. Transparent CeO(2)/polycarbonate surfaces that prevent adhesion, proliferation, and spread of Pseudomonas aeruginosa PA14 were manufactured. Large amounts of monodisperse CeO(2) nanoparticles were synthesized in segmented flow using a high-throughput microfluidic benchtop system using water/benzyl alcohol mixtures and oleylamine as capping agent. This reduced the reaction time for nanoceria by more than one order of magnitude compared to conventional batch methods. Ceria nanoparticles prepared by segmented flow showed high catalytic activity in halogenation reactions, which makes them highly efficient functional mimics of haloperoxidase enzymes. Haloperoxidases are used in nature by macroalgae to prevent formation of biofilms via halogenation of signaling compounds that interfere with bacterial cell–cell communication (“quorum sensing”). CeO(2)/polycarbonate nanocomposites were prepared by dip-coating plasma-treated polycarbonate panels in CeO(2) dispersions. These showed a reduction in bacterial biofilm formation of up to 85% using P. aeruginosa PA14 as model organism. Besides biofilm formation, also the production of the virulence factor pyocyanin in is under control of the entire quorum sensing systems P. aeruginosa. CeO(2)/PC showed a decrease of up to 55% in pyocyanin production, whereas no effect on bacterial growth in liquid culture was observed. This indicates that CeO(2) nanoparticles affect quorum sensing and inhibit biofilm formation in a non-biocidal manner

Two Iranian families with a novel mutation in GJB2 causing autosomal dominant nonsyndromic hearing loss

Mutations in GJB2 , encoding connexin 26 (Cx26), cause both autosomal dominant and autosomal recessive nonsyndromic hearing loss (ARNSHL) at the DFNA3 and DFNB1 loci, respectively. Most of the over 100 described GJB2 mutations cause ARNSHL. Only a minority has been associated with autosomal dominant hearing loss. In this study, we present two families with autosomal dominant nonsyndromic hearing loss caused by a novel mutation in GJB2 (p.Asp46Asn). Both families were ascertained from the same village in northern Iran consistent with a founder effect. This finding implicates the D46N missense mutation in Cx26 as a common cause of deafness in this part of Iran mandating mutation screening of GJB2 for D46N in all persons with hearing loss who originate from this geographic region. © 2011 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83755/1/33209_ftp.pd