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

Dagger Categories of Tame Relations

Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and inner product on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with "tame" relations as morphisms. Examples include familiar categories in the foundations of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

Membrane Systems and Hypercomputation

We present a brief analysis of hypercomputation and its relationship to membrane systems theory, including a re-evaluation of Turing’s analysis of computation and the importance of timing structure, and suggest a ‘cosmological’ variant of tissue P systems that is capable of super-Turing behaviour. No prior technical background in hypercomputation theory is assumed

Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups

One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the corresponding undeformed universal envelope. Consequently, these contracted QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we consider kappa-Poincare in 3 and 4 spacetime dimensions.Comment: 32 page

The Intentional Use of Service Recovery Strategies to Influence Consumer Emotion, Cognition and Behaviour

Service recovery strategies have been identified as a critical factor in the success of. service organizations. This study develops a conceptual frame work to investigate how specific service recovery strategies influence the emotional, cognitive and negative behavioural responses of . consumers., as well as how emotion and cognition influence negative behavior. Understanding the impact of specific service recovery strategies will allow service providers' to more deliberately and intentionally engage in strategies that result in positive organizational outcomes. This study was conducted using a 2 x 2 between-subjects quasi-experimental design. The results suggest that service recovery has a significant impact on emotion, cognition and negative behavior. Similarly, satisfaction, negative emotion and positive emotion all influence negative behavior but distributive justice has no effect

Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcome

Inverse scattering and the chiral equation

SIGLEAvailable from British Library Document Supply Centre- DSC:D85890 / BLDSC - British Library Document Supply CentreGBUnited Kingdo