On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Insights into the morphology of the Serra da Cangalha impact structure from geophysical modeling

Forward modeling is commonly applied to gravity field data of impact structures to determine the main gravity anomaly sources. In this context, we have developed 2.5-D gravity models of the Serra da Cangalha impact structure for the purpose of investigating geological bodies/structures underneath the crater. Interpretation of the models was supported by ground magnetic data acquired along profiles, as well as by high resolution aeromagnetic data. Ground magnetic data reveal the presence of short-wavelength anomalies probably related to shallow magnetic sources that could have been emplaced during the cratering process. Aeromagnetic data show that the basement underneath the crater occurs at an average depth of about 1.9 km, whereas in the region beneath the central uplift it is raised to 0.51 km below the current surface. These depths are also supported by 2.5-D gravity models showing a gentle relief for the basement beneath the central uplift area. Geophysical data were used to provide further constraints for numeral modeling of crater formation that provided important information on the structural modification that affected the rocks underneath the crater, as well as on shock-induced modifications of target rocks. The results showed that the morphology is consistent with the current observations of the crater and that Serra da Cangalha was formed by a meteorite of approximately 1.4 km diameter striking at 12 km s-1.

Haemodynamic effects of aliskiren in decompensated severe heart failure

Aim: The renin-angiotensin-aldosterone system (RAAS) has dual pathways to angiotensin II production; therefore, multiple blockages may be useful in heart failure. In this study, we evaluated the short-term haemodynamic effects of aliskiren, a direct renin inhibitor, in patients with decompensated severe heart failure who were also taking angiotensin-converting enzyme ( ACE) inhibitors. Materials and methods: A total of 16 patients (14 men, two women, mean age: 60.3 years) were enrolled in the study. The inclusion criteria included hospitalisation due to decompensated heart failure, ACE inhibitor use, and an ejection fraction < 40% (mean: 21.9 +/- 6.7%). The exclusion criteria were: creatinine > 2.0 mg/dl, cardiac pacemaker, serum K+ > 5.5 mEq/l, and systolic blood pressure < 70 mmHg. Patients either received 150 mg/d aliskiren for 7 days (aliskiren group, n = 10) or did not receive aliskiren (control group, n = 6). Primary end points were systemic vascular resistance and cardiac index values. Repeated-measures analysis of variance (ANOVA) was used to assess variables before and after intervention. A two-sided p-value < 0.05 was considered statistically significant. Results: Compared to pre-intervention levels, systemic vascular resistance was reduced by 20.4% in aliskiren patients, but it increased by 2.9% in control patients (p = 0.038). The cardiac index was not significantly increased by 19.0% in aliskiren patients, but decreased by 8.4% in control patients (p = 0.127). No differences in the pulmonary capillary or systolic blood pressure values were observed between the groups. Conclusion: Aliskiren use reduced systemic vascular resistance in patients with decompensated heart failure taking ACE inhibitors.

Transiting exoplanets from the CoRoT space mission XXI. CoRoT-19b: a low density planet orbiting an old inactive F9V-star

Context. Observations of transiting extrasolar planets are of key importance to our understanding of planets because their mass, radius, and mass density can be determined. These measurements indicate that planets of similar mass can have very different radii. For low-density planets, it is generally assumed that they are inflated owing to their proximity to the host-star. To determine the causes of this inflation, it is necessary to obtain a statistically significant sample of planets with precisely measured masses and radii. Aims. The CoRoT space mission allows us to achieve a very high photometric accuracy. By combining CoRoT data with high-precision radial velocity measurements, we derive precise planetary radii and masses. We report the discovery of CoRoT-19b, a gas-giant planet transiting an old, inactive F9V-type star with a period of four days. Methods. After excluding alternative physical configurations mimicking a planetary transit signal, we determine the radius and mass of the planet by combining CoRoT photometry with high-resolution spectroscopy obtained with the echelle spectrographs SOPHIE, HARPS, FIES, and SANDIFORD. To improve the precision of its ephemeris and the epoch, we observed additional transits with the TRAPPIST and Euler telescopes. Using HARPS spectra obtained during the transit, we then determine the projected angle between the spin of the star and the orbit of the planet. Results. We find that the host star of CoRoT-19b is an inactive F9V-type star close to the end of its main-sequence life. The host star has a mass M-* = 1.21 +/- 0.05 M-circle dot and radius R-* = 1.65 +/- 0.04 R-circle dot. The planet has a mass of M-P = 1.11 +/- 0.06 M-Jup and radius of R-P = 1.29 +/- 0.03 R-Jup. The resulting bulk density is only rho = 0.71 +/- 0.06 g cm (3), which is much lower than that for Jupiter. Conclusions. The exoplanet CoRoT-19b is an example of a giant planet of almost the same mass as Jupiter but a approximate to 30% larger radius.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Uso da monitorização hemodinâmica contínua não invasiva na insuficiência cardíaca descompensada

FUNDAMENTO: A avaliação clínico-hemodinâmica à beira do leito e o uso do cateter de artéria pulmonar para a estimativa de dados hemodinâmicos têm sido utilizados na insuficiência cardíaca descompensada. Entretanto, não existem dados com o uso da monitorização hemodinâmica contínua não invasiva. OBJETIVO: Comparar as medidas obtidas com a monitorização hemodinâmica não invasiva com as invasivas em pacientes com insuficiência cardíaca descompensada e refratária ao tratamento. MÉTODOS: As medidas hemodinâmicas não invasivas foram obtidas através da monitorização contínua da pressão arterial sistêmica pelo modelo de ondas de pulso (modelflow) e foram comparadas com as medidas obtidas pela passagem do cateter de artéria pulmonar, simultaneamente. RESULTADOS: Foram realizadas 56 medidas em 14 pacientes estudados em dias e horários diferentes. O índice de correlação entre as medidas da pressão arterial sistólica foi de r = 0,26 (IC 95% = 0,00 a 0,49, p = 0,0492) e da diastólica de r = 0,50 (IC 95% = 0,27 a 0,67, p < 0,0001). A correlação foi de r = 0,55 (IC 95% = 0,34 a 0,71, p 0,0001) para o índice cardíaco e de r = 0,32 (IC 95% = 0,06 a 0,53, p = 0,0178) para a resistência vascular sistêmica. CONCLUSÃO: Houve correlação entre as medidas hemodinâmicas não invasivas quando comparadas às medidas do cateter de artéria pulmonar. A monitorização hemodinâmica contínua não invasiva pode ser útil para pacientes internados com insuficiência cardíaca descompensada.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

A variational approach to camera motion smoothing

[EN] In this paper we study a variational problem derived from a computer vision application: video camera calibration with smoothing constraint. By video camera calibration we meanto estimate the location, orientation and lens zoom-setting of the camera for each video frame taking into account image visible features. To simplify the problem we assume that the camera is mounted on a tripod, in such case, for each frame captured at time t , the calibration is provided by 3 parameters : (1) P(t) (PAN) which represents the tripod vertical axis rotation, (2) T(t) (TILT) which represents the tripod horizontal axis rotation and (3) Z(t) (CAMERA ZOOM) the camera lens zoom setting. The calibration function t -> u(t) = (P(t),T(t),Z(t)) is obtained as the minima of an energy function I[u] . In thIs paper we study the existence of minima of such energy function as well as the solutions of the associated Euler-Lagrange equations.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Dense disparity map estimation respecting image discontinuities

[EN] We present an energy based approach to estimate a dense disparity map from a set of two weakly calibrated stereoscopic images while preserving its discontinuities resulting from image boundaries. We first derive a simplified expression for the disparity that allows us to estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method The resulting parabolic problem has a unique solution. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scalespace. Experimental results on both synthetic and real images arere presented to illustrate the capabilities of this PDE and scale-space based method.

A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.