Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

The BRST quantization and the no-ghost theorem for AdS_3

In our previous papers, we prove the no-ghost theorem without light-cone directions (hep-th/0005002, hep-th/0303051). We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS_3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS_3. The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form.Comment: 22 pages, JHEP and AMS-LaTeX; v2 & 3: minor improvement

Gauge-invariant gravitational wave modes in pre-big bang cosmology

The t<0 branch of pre-big bang cosmological scenarios is subject to a gravitational wave instability. The unstable behaviour of tensor perturbations is derived in a very simple way in Hwang's covariant and gauge-invariant formalism developed for extended theories of gravity. A simple interpretation of this instability as the effect of an "antifriction" is given, and it is argued that a universe must eventually enter the expanding phase.Comment: 4 pages, latex, to appear in Eur. Phys. J.

Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"

In a recent paper Gutiérrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general

Recommended Finite Element Formulations for the Analysis of Off-shore Blast Walls in an Explosion

This study suggests relevant finite element (FE) formulations for the structural analysis of offshore blast walls subjected to blast loadings due to hydrocarbon explosions. The present blast wall model adopted from HSE (2003) consists of a corrugated panel and supporting members, and was modelled with shell, thick-shell, and solid element combinations in LS-DYNA, an explicit finite element analysis (FEA) solver. Stainless and mild steels were employed as materials for the blast wall model, with consideration of strain rate effect throughout ten (10) pulse pressure load regimes. The obtained FEA results were validated by experimental data from HSE (2003) with decent agreement. In the present study, recommended FE formulations with additional hourglass control functions were widely discussed from the perspectives of solution accuracy and computational cost based on a statistical approach. The obtained outcomes could be used for the structural analysis and design of offshore blast walls in the estimations of maximum and permanent deformations under blast loadings.111Ysciescopu

Non-linear corrections to inflationary power spectrum

We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum completely dominates and leading non-linear corrections remain totally negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour of the non-linear corrections.Comment: (v1) 14 pages, 2 figures; (v2) references added and discussions expanded, including a new version of Figure 2, to appear in Journal of Cosmology and Astroparticle Physic

BRST Quantization of String Theory in AdS(3)

We study the BRST quantization of bosonic and NSR strings propagating in AdS(3) x N backgrounds. The no-ghost theorem is proved using the Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations of affine SL(2,R) appear on an equal footing. Possible generalizations to related curved backgrounds are discussed.Comment: JHEP style, 23 pages; v2:minor changes and references added; v3: typos corrected, version to appear in JHEP; v4: one reference adde

Low-scale Quintessential Inflation

In quintessential inflationary model, the same master field that drives inflation becomes, later on, the dynamical source of the (present) accelerated expansion. Quintessential inflationary models require a curvature scale at the end of inflation around $10^{-6}M_{\rm P}$ in order to explain the large scale fluctuations observed in the microwave sky. If the curvature scale at the end of inflation is much smaller than $10^{-6}M_{\rm P}$, the large scale adiabatic mode may be produced thanks to the relaxation of a scalar degree of freedom, which will be generically denoted, according to the recent terminology, as the curvaton field. The production of the adiabatic mode is analysed in detail in the case of the minimal quintessential inflationary model originally proposed by Peebles and Vilenkin.Comment: 25 pages; 5 figure

Density Perturbations in the Ekpyrotic Scenario

We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a `bounce' to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation amplitude is typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file. Minor typographical and numerical errors corrected, discussion added. This version to appear in Physical Review

Remote oil spill detection and monitoring on ice-covered waters

The spillage of oil in Polar Regions is particularly serious due to the threat to the environment and the difficulties in detecting and tracking the full extent of the oil seepage beneath the sea ice. Development of fast and reliable sensing techniques is highly desirable. In this paper hyperspectral imaging is proposed as a potential tool to detect the presence of oil beneath the sea ice. A feasibility study project was initiated to explore the detectability of the oil under ice layer. Some preliminary results obtained during this project are discussed