Duality Principle and Braided Geometry

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided geometry.Comment: 24 page

Impervious surface estimation using remote sensing images and gis : how accurate is the estimate at subdivision level?

Impervious surface has long been accepted as a key environmental indicator linking development to its impacts on water. Many have suggested that there is a direct correlation between degree of imperviousness and both quantity and quality of water. Quantifying the amount of impervious surface, however, remains difficult and tedious especially in urban areas. Lately more efforts have been focused on the application of remote sensing and GIS technologies in assessing the amount of impervious surface and many have reported promising results at various pixel levels. This paper discusses an attempt at estimating the amount of impervious surface at subdivision level using remote sensing images and GIS techniques. Using Landsat ETM+ images and GIS techniques, a regression tree model is first developed for estimating pixel imperviousness. GIS zonal functions are then used to estimate the amount of impervious surface for a sample of subdivisions. The accuracy of the model is evaluated by comparing the model-predicted imperviousness to digitized imperviousness at the subdivision level. The paper then concludes with a discussion on the convenience and accuracy of using the method to estimate imperviousness for large areas

Almost commutative Riemannian geometry: wave operators

Associated to any (pseudo)-Riemannian manifold $M$ of dimension $n$ is an $n+1$-dimensional noncommutative differential structure (\Omega^1,\extd) on the manifold, with the extra dimension encoding the classical Laplacian as a noncommutative `vector field'. We use the classical connection, Ricci tensor and Hodge Laplacian to construct (\Omega^2,\extd) and a natural noncommutative torsion free connection $(\nabla,\sigma)$ on $\Omega^1$. We show that its generalised braiding \sigma:\Omega^1\tens\Omega^1\to \Omega^1\tens\Omega^1 obeys the quantum Yang-Baxter or braid relations only when the original $M$ is flat, i.e their failure is governed by the Riemann curvature, and that \sigma^2=\id only when $M$ is Einstein. We show that if $M$ has a conformal Killing vector field $\tau$ then the cross product algebra $C(M)\rtimes_\tau\R$ viewed as a noncommutative analogue of $M\times\R$ has a natural $n+2$-dimensional calculus extending $\Omega^1$ and a natural spacetime Laplacian now directly defined by the extra dimension. The case $M=\R^3$ recovers the Majid-Ruegg bicrossproduct flat spacetime model and the wave-operator used in its variable speed of light preduction, but now as an example of a general construction. As an application we construct the wave operator on a noncommutative Schwarzschild black hole and take a first look at its features. It appears that the infinite classical redshift/time dilation factor at the event horizon is made finite.Comment: 39 pages, 4 pdf images. Removed previous Sections 5.1-5.2 to a separate paper (now ArXived) to meet referee length requirements. Corresponding slight restructure but no change to remaining conten

Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups $U_q(g)$. They have the same FRT generators $l^\pm$ but a matrix braided-coproduct \und\Delta L=L\und\tens L where $L=l^+Sl^-$, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices $BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double D(\usl) (also known as the `quantum Lorentz group') is the semidirect product as an algebra of two copies of \usl, and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction

Does financial development cause economic growth in the ASEAN-4 countries

This paper empirically examines the short- and long-run finance-growth nexus during the post-1997 financial crisis in the ASEAN-4 countries (i.e., Indonesia,Malaysia, Thailand and the Philippines) by employing battery of times series techniques such as autoregressive distributed lag (ARDL) model, vector error correction model (VECM), variance decompositions (VDCs) and impulseresponse functions (IRFs). Based on the ARDL models, the study documents a long-run equilibrium between economic growth, finance depth, share of investment and inflation. The study also finds that the common sources of economic progress/regress among the countries are price stability and financial development. Granger causality tests based on the VECM further reveals that there are: (i) no causality between finance-growth in Indonesia; the finding in favour of “the independent hypothesis” of Lucas (1988); (ii) a unidirectional causality running from finance to growth in Malaysia, thus supporting “the finance-growth led hypothesis” or “the supply-leading view”; (iii) a bidirectional causality between finance-growth in Thailand, the finding accords with “the feedback hypothesis” or “bidirectional causality view”; and (iv) a unidirectional causality stemming from growth to finance in the Philippines, the finding echoes with “the growth-led finance hypothesis” or “the demand following view” of Robinson (1952). Based on the VDCs and IRFs, the study discovers that the variations in the economic growth rely very much on its own innovations. If policy makers want to promote growth in the ASEAN-4 countries, priority should be given for long run policies, i.e., the enhancement of existing financial institutions both in the banking sector and stock market

Projective module description of the q-monopole

The Dirac q-monopole connection is used to compute projector matrices of quantum Hopf line bundles for arbitrary winding number. The Chern-Connes pairing of cyclic cohomology and K-theory is computed for the winding number -1. The non-triviality of this pairing is used to conclude that the quantum principal Hopf fibration is non-cleft. Among general results, we provide a left-right symmetric characterization of the canonical strong connections on quantum principal homogeneous spaces with an injective antipode. We also provide for arbitrary strong connections on algebraic quantum principal bundles (Hopf-Galois extensions) their associated covariant derivatives on projective modules.Comment: AMS-LaTeX 18 pages, no figures, correction of the Chern-number-sign-change Comments, 6 pages of new contents adde