TRAVELLING THROUGH PITCH SPACE SPEEDS UP MUSICAL TIME

SEVERAL MODELS OF TIME ESTIMATION HAVE BEEN developed in psychology; a few have been applied to music. In the present study, we assess the influence of the distances travelled through pitch space on retrospective time estimation. Participants listened to an isochronous chord sequence of 20-s duration. They were unexpectedly asked to reproduce the time interval of the sequence. The harmonic structure of the stimulus was manipulated so that the sequence either remained in the same key (CC) or travelled through a closely related key (CFC) or distant key (CGbC). Estimated times were shortened when the sequence modulated to a very distant key. This finding is discussed in light of Lerdahl's Tonal Pitch Space Theory (2001), Firmino and Bueno's Expected Development Fraction Model (in press), and models of time estimation.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Synthesis, characterization and electrochemical behavior of the vanadium pentoxide/cetyl pyridinium chloride hybrid material

In situ and ex situ studies concerning the new hybrid material vanadium pentoxide xerogel in the presence of the cationic surfactant cetyl pyridinium chloride (V(2)O(5)/CPC) are presented. The in situ characterization studies revealed the presence of a lamellar structure for the V(2)O(5)/CPC hybrid material. The intercalation reaction was evidenced on the basis of the increase in the d-spacing as well as the displacement of the infrared bands toward lower energy levels. Electrochemical studies comprising the cyclic voltammetry and the electrochemical impedance spectroscopy techniques showed that the behavior of the hybrid material is considerably influenced by the electrolyte composition. The ion insertion/de-insertion into the V(2)O(5) xerogel structure accompanying the charge transfer process is influenced by the solid-state diffusion process modeled by using the finite-space Warburg element.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Contribution to the ground-based follow-up of the Gaia space mission

The Gaia Space Mission [Mignard, F., 2005. The three-dimensional universe with Gaia. ESA/SP-576; Perryman, M., 2005. The three-dimensional universe with Gaia. ESA/SP-576] will observe several transient events as supernovae, microlensing, gamma ray bursts and new Solar System objects. The satellite, due to its scanning law, will detect these events but will not be able to monitor them. So, to take these events into consideration and to perform further studies it is necessary to follow them with Earth-based observations. These observations could be efficiently done by a ground-based network of well-equipped telescopes scattered in both hemispheres. Here we focus our attention at the new Solar System objects to be discovered and observed by the Gaia satellite [Mignard, F., 2002. Observations of Solar System objects by Gaia I. Detection of NEOS. Astron. Astrophys. 393, 727] mainly asteroids, NEOs and comets. A dedicated ground-based network of telescopes as proposed by Thuillot [2005. The three-dimensional universe with Gaia. ESA/SP-576] will allow to monitor those events, to avoid losing them and to perform a quick characterization of some physical properties which will be important for the identification of these objects in further measurements by Gaia. We present in this paper, the beginning of the organization of a Latin-American ground-based network of telescopes and observers joining several institutions in Argentina, Bolivia, Brazil and other Latin-American countries aiming to contribute to the follow-up of Gaia science alerts for Solar System objects. (C) 2008 Elsevier Ltd. All rights reserved.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Color-flavor locked strange matter and strangelets at finite temperature

It is possible that a system composed of up, down, and strange quarks exists as the true ground state of nuclear matter at high densities and low temperatures. This exotic plasma, called strange quark matter (SQM), seems to be even more favorable energetically if quarks are in a superconducting state, the so-called color-flavor locked state. Here we present calculations made on the basis of the MIT bag model, considering the influence of finite temperature on the allowed parameters characterizing the system for stability of bulk SQM (the so-called stability windows) and also for strangelets, small lumps of SQM, both in the color-flavor locking scenario. We compare these results with the unpaired SQM and also briefly discuss some astrophysical implications of them. Also, the issue of the strangelet's electric charge is discussed. The effects of dynamical screening, though important for nonpaired SQM strangelets, are not relevant when considering pairing among all three flavors and colors of quarks.

Transiting exoplanets from the CoRoT space mission XVIII. CoRoT-18b: a massive hot Jupiter on a prograde, nearly aligned orbit

We report the detection of CoRoT-18b, a massive hot Jupiter transiting in front of its host star with a period of 1.9000693 +/- 0.0000028 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite combined with spectroscopic and photometric ground-based follow-up observations. The planet has a mass M(p) = 3.47 +/- 0.38 M(Jup), a radius R(p) = 1.31 +/- 0.18 R(Jup), and a density rho(p) = 2.2 +/- 0.8 g cm(-3). It orbits a G9V star with a mass M(*) = 0.95 +/- 0.15 M(circle dot), a radius R(*) = 1.00 +/- 0.13 R(circle dot), and a rotation period P(rot) = 5.4 +/- 0.4 days. The age of the system remains uncertain, with stellar evolution models pointing either to a few tens Ma or several Ga, while gyrochronology and lithium abundance point towards ages of a few hundred Ma. This mismatch potentially points to a problem in our understanding of the evolution of young stars, with possibly significant implications for stellar physics and the interpretation of inferred sizes of exoplanets around young stars. We detected the RossiterMcLaughlin anomaly in the CoRoT-18 system thanks to the spectroscopic observation of a transit. We measured the obliquity psi = 20 degrees +/- 20 degrees +/- (sky-projected value lambda = -10 degrees +/- 20 degrees), indicating that the planet orbits in the same way as the star is rotating and that this prograde orbit is nearly aligned with the stellar equator.

Transiting exoplanets from the CoRoT space mission XIII. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content

We announce the discovery of the transiting planet CoRoT-13b. Ground-based follow-up in CFHT and IAC80 confirmed CoRoT's observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm(-3). It orbits a G0V star with T(eff) = 5 945 K, M(*) = 1.09 M(circle dot), R(*) = 1.01 R(circle dot), solar metallicity, a lithium content of +1.45 dex, and an estimated age of between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass, implies that heavy elements are present with a mass of between about 140 and 300 M(circle plus).

Transiting exoplanets from the CoRoT space mission X. CoRoT-10b: a giant planet in a 13.24 day eccentric orbit

Context. The space telescope CoRoT searches for transiting extrasolar planets by continuously monitoring the optical flux of thousands of stars in several fields of view. Aims. We report the discovery of CoRoT-10b, a giant planet on a highly eccentric orbit (e = 0.53 +/- 0.04) revolving in 13.24 days around a faint (V = 15.22) metal-rich K1V star. Methods. We used CoRoT photometry, radial velocity observations taken with the HARPS spectrograph, and UVES spectra of the parent star to derive the orbital, stellar, and planetary parameters. Results. We derive a radius of the planet of 0.97 +/- 0.07 R(Jup) and a mass of 2.75 +/- 0.16 M(Jup). The bulk density,rho(p) = 3.70 +/- 0.83 g cm(-3), is similar to 2.8 that of Jupiter. The core of CoRoT-10b could contain up to 240 M(circle plus) of heavy elements. Moving along its eccentric orbit, the planet experiences a 10.6-fold variation in insolation. Owing to the long circularisation time, tau(circ) > 7 Gyr, a resonant perturber is not required to excite and maintain the high eccentricity of CoRoT-10b.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.