Improved bounds on the set A(A+1)

For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime order, or the real line. In the finite field case we show that A(A+1) is of cardinality at least C|A|^{57/56-o(1)} for some absolute constant C, so long as |A| < p^{1/2}. In the real case we show that the cardinality is at least C|A|^{24/19-o(1)}. These improve on the previously best-known exponents of 106/105-o(1) and 5/4 respectively

An improved algorithm for optimum structural design with multiple frequency constraints

An optimality criterion (OC) method for minimum-weight design of structures having multiple constraints on natural frequencies is presented. In this work a new resizing strategy is developed based on relaxation techniques. A computationally adaptive control parameter is used in conjunction with existing OC recursive formulae to promote convergence of optimum structural designs. Some considerations regarding the coupling of the modified Aitken accelerator with the OC method are discussed. Improved and rapidly converged minimum-weight designs are obtained when using an under-relaxed recursive scheme combined with the modified Aitken accelerator

Extragalactic Source Counts in the Spitzer 24-micron Band: What Do We Expect From ISOCAM 15-micron Data and Models?

The comparison between the new Spitzer data at 24 micron and the previous ISOCAM data at 15 micron is a key tool to understand galaxy properties and evolution in the infrared and to interpret the observed number counts, since the combination of Spitzer with the ISO cosmological surveys provides for the first time the direct view of the Universe in the Infrared up to z~2. We present the prediction in the Spitzer 24-micron band of a phenomenological model for galaxy evolution derived from the 15-micron data. Without any ``a posteriori'' update, the model predictions seem to agree well with the recently published 24-micron extragalactic source counts, suggesting that the peak in the 24-micron counts is dominated by ``starburst'' galaxies like those detected by ISOCAM at 15 micron, but at higher redshifts (1 < z < 2 instead of 0.5 < z < 1.5).Comment: 8 pages: 4 pages of main text + 5 postscript figures, use aastex. Accepted for publication in ApJL. Replaced with the proof version (added missing references and corrected a few sentences

Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fiber

We report on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fiber interferometer. The Kerr nonlinearity in the fiber is exploited for the generation of two independent squeezed beams. These interfere at a beam splitter and EPR entanglement is obtained between the output beams. The correlation of the amplitude (phase) quadratures is measured to be 4.0±0.2 (4.0±0.4)dB below the quantum noise limit. The sum criterion for these squeezing variances 0.80±0.03<2 verifies the nonseparability of the state. The product of the inferred uncertainties for one beam (0.64±0.08) is well below the EPR limit of unity

Cosmic bulk viscosity through backreaction

We consider an effective viscous pressure as the result of a backreaction of inhomogeneities within Buchert's formalism. The use of an effective metric with a time-dependent curvature radius allows us to calculate the luminosity distance of the backreaction model. This quantity is different from its counterpart for a "conventional" spatially flat bulk viscous fluid universe. Both expressions are tested against the SNIa data of the Union2.1 sample with only marginally different results for the distance-redshift relation and in accordance with the $\Lambda$CDM model. Future observations are expected to be able to discriminate among these models on the basis of indirect measurements of the curvature evolution.Comment: 18 pages, 6 figures, comments and references added, accepted for publication in GR

Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models

We exhibit a mapping identifying Kitaev's quantum double lattice models explicitly as a subclass of Levin and Wen's string net models via a completion of the local Hilbert spaces with auxiliary degrees of freedom. This identification allows to carry over to these string net models the representation-theoretic classification of the excitations in quantum double models, as well as define them in arbitrary lattices, and provides an illustration of the abstract notion of Morita equivalence. The possibility of generalising the map to broader classes of string nets is considered.Comment: 8 pages, 6 eps figures; v2: matches published versio

Enhancement of W+/- H-/+ Production at Hadron Colliders in the Two Higgs Doublet Model

We discuss the associated W+/- H-/+ production at the CERN Large Hadron Collider. The dependence of the hadronic cross section on the Higgs sector parameters is investigated in detail in the framework of the general Two Higgs Doublet Model (THDM). We study the possible enhancement of the THDM prediction for the cross section compared to the prediction of the Minimal Supersymmetric Standard Model (MSSM). We find regions in the THDM parameter space where the THDM prediction can exceed the one of the MSSM by two orders of magnitude. These regions of large cross section are in agreement with theoretical bounds on the model, derived from the requirement of vacuum stability and perturbative unitarity, and are not excluded by experimental constraints.Comment: 19 pages, 5 figure

RAO-II: an AUV for underwater inspection

AIRSUB is a research project funded by the Spanish Ministry of Science and Technology whose aim is to explore the industrial applications of underwater robots. The Systems, Robotics and Vision Group (SRV) from the University of the Balearic Islands (UIB) is responsible for the subproject of cable/pipeline inspection [1]. To this purpose, an Autonomous Underwater Vehicle (AUV) is under development as a platform to test the vision algorithms, control strategies and software architectures devised in the last years. This paper describes the main characteristics of the new platform, which is based on a commercial Remotely Operated Vehicle (ROV). The original vehicle has been deeply modifi ed in structure as well as in its electric, electronic and sensorial facets to obtain fully autonomous operation

On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory

Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P^1-spectrum MGL of Voevodsky is considered as a commutative P^1-ring spectrum. There is a unique ring morphism MGL^{2*,*}(k)--> Z which sends the class [X]_{MGL} of a smooth projective k-variety X to the Euler characteristic of the structure sheaf of X. Our main result states that there is a canonical grade preserving isomorphism of ring cohomology theories MGL^{*,*}(X,U) \tensor_{MGL^{2*,*}(k)} Z --> K^{TT}_{- *}(X,U) = K'_{- *}(X-U)} on the category of smooth k-varieties, where K^{TT}_* is Thomason-Trobaugh K-theory and K'_* is Quillen's K'-theory. In particular, the left hand side is a ring cohomology theory. Moreover both theories are oriented and the isomorphism above respects the orientations. The result is an algebraic version of a theorem due to Conner and Floyd. That theorem reconstructs complex K-theory via complex cobordism.Comment: LaTeX, 18 pages, uses XY-pi