The construction of translation planes from projective spaces

AbstractCan every (nonDesarguesian) projective plane be imbedded (in some natural, geometric fashion) in a (Desarguesian) projective space? The question is new but important, for, if the answer is yes, two entirely separate fields of research can be united. This paper provides a conceptually simple geometric construction which yields an affirmative answer for a broad class of planes. A plane π is given by the construction precisely when π is a translation plane with a coordinatizing right Veblen-Wedderburn system which is finite-dimensional over its left-operator skew-field. The condition is satisfied by all known translation planes, including all finite translation planes

Modification to the power spectrum in the brane world inflation driven by the bulk inflaton

We compute the cosmological perturbations generated in the brane world inflation driven by the bulk inflaton. Different from the model that the inflation is a brane effect, we exhibit the modification of the power spectrum of scalar perturbations due to the existence of the fifth dimension. With the change of the initial vacuum, we investigate the dependence of the correction of the power spectrum on the choice of the vacuum.Comment: replaced with the revised version, accepted for publication in PR

Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page

Age Constraints on Brane Models of Dark Energy

Inspired by recent developments in particle physics, the so-called brane world cosmology seems to provide an alternative explanation for the present dark energy problem. In this paper, we use the estimated age of high-$z$ objects to constrain the value of the cosmological parameters in some particular scenarios based on this large scale modification of gravity. We show that such models are compatible with these observations for values of the crossover distance between the 4 and 5 dimensions of the order of $r_c \leq 1.67H_o^{-1}$.Comment: 4 pages, 2 figures, 1 table, to appear in Phys. Rev.

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references adde

Brane World Cosmologies and Statistical Properties of Gravitational Lenses

Brane world cosmologies seem to provide an alternative explanation for the present accelerated stage of the Universe with no need to invoke either a cosmological constant or an exotic \emph{quintessence} component. In this paper we investigate statistical properties of gravitational lenses for some particular scenarios based on this large scale modification of gravity. We show that a large class of such models are compatible with the current lensing data for values of the matter density parameter $\Omega_{\rm{m}} \leq 0.94$ ($1\sigma$). If one fixes $\Omega_{\rm{m}}$ to be $\simeq 0.3$, as suggested by most of the dynamical estimates of the quantity of matter in the Universe, the predicted number of lensed quasars requires a slightly open universe with a crossover distance between the 4 and 5-dimensional gravities of the order of $1.76 H_o^{-1}$.Comment: 6 pages, 3 figures, revte

Strategic positioning:an integrated decision process for manufacturers

Purpose – This paper describes research that has sought to create a formal and rational process that guides manufacturers through the strategic positioning decision. Design/methodology/approach – The methodology is based on a series of case studies to develop and test the decision process. Findings – A decision process that leads the practitioner through an analytical process to decide which manufacturing activities they should carryout themselves. Practical implications – Strategic positioning is concerned with choosing those production related activities that an organisations should carry out internally, and those that should be external and under the ownership and control of suppliers, partners, distributors and customers. Originality/value – This concept extends traditional decision paradigms, such as those associated with “make versus buy” and “outsourcing”, by looking at the interactions between manufacturing operations and the wider supply chain networks associated with the organisation

Some Observational Consequences of Brane World Cosmologies

The presence of dark energy in the Universe is inferred directly and indirectly from a large body of observational evidence. The simplest and most theoretically appealing possibility is the vacuum energy density (cosmological constant). However, although in agreement with current observations, such a possibility exacerbates the well known cosmological constant problem, requiring a natural explanation for its small, but nonzero, value. In this paper we focus our attention on another dark energy candidate, one arising from gravitational \emph{leakage} into extra dimensions. We investigate observational constraints from current measurements of angular size of high-$z$ compact radio-sources on accelerated models based on this large scale modification of gravity. The predicted age of the Universe in the context of these models is briefly discussed. We argue that future observations will enable a more accurate test of these cosmologies and, possibly, show that such models constitute a viable possibility for the dark energy problem.Comment: 6 pages, 4 figures, to appear in Phys. Rev. D (minor revisions

The Dynamics of Brane-World Cosmological Models

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall-Sundrum-type models are self-consistent and simple and allow for an investigation of the essential non-linear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ

Theory of Cosmological Perturbations and Applications to Superstring Cosmology

The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an introduction to this theory, beginning with an overview of the Newtonian theory of fluctuations, moving on to the analysis of fluctuations in the realm of classical general relativity, and culminating with a discussion of the quantum theory of cosmological perturbations. I will illustrate the formalism with applications to inflationary cosmology. I will review the basics of inflationary cosmology and discuss why - through the evolution of fluctuations - inflation may provide a way of observationally testing Planck-scale physics.Comment: Writeup of lectures delivered at the 2004 Cargese Summer School on String Theory, 49 pages, 3 figure