Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case

The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined {\em affine degree} of the equation system. Replacing the affine degree of the equation system by a suitably defined {\em real degree} of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.Comment: Late

Structural characters of epidermal cell walls and resistance to powdery mildew of different grapevine cultivars

The analysis of 12 grapevine cultivars differing in susceptibility to powdery mildew revealed a correlation between the thickness of cuticle plus cell wall of young leaves and resistance to mildew. Neither in mature leaves or in leaves of in vitro plants or in berries such correlations could be established. Coating of the leaf surface with a polymetacrylate antitranspirant prevented sporulation in all cases, although infection structures were formed

Orbit Determination of Close Binary Systems using Lucky Imaging

We present relative positions of visual binaries observed during 2009 with the FastCam "lucky-imaging" camera at the 1.5-m Carlos Sanchez Telescope (TCS) at the Observatorio del Teide. We obtained 424 CCD observations (averaged in 198 mean relative positions) of 157 binaries with angular separations in the range 0.14-15.40", with a median separation of 0.51". For a given system, each CCD image represents the sum of the best 10-25% images from 1000-5000 short-exposure frames. Derived internal errors were 7 mas in r and 1.2^{\circ} (9 mas) in q. When comparing to systems with very well-known orbits, we find that the rms deviation in r residuals is 23 mas, while the rms deviation in q residuals is 0.73 deg/r. We confirmed 18 Hipparcos binaries and we report new companions to BVD 36 A and J 621 B. For binaries with preliminary orbital parameters, the relative radial velocity was estimated as well. We also present four new revised orbits computed for LDS 873, BU 627 A-BC, BU 628 and HO 197 AB. This work is the first results on visual binaries using the FastCam lucky-imaging camera.Comment: 23 pages, 10 figures, 14 tables, accepted August 18th, 2011, to be published in MNRA

The High Angular Resolution Multiplicity of Massive Stars

We present the results of a speckle interferometric survey of Galactic massive stars that complements and expands upon a similar survey made over a decade ago. The speckle observations were made with the KPNO and CTIO 4 m telescopes and USNO speckle camera, and they are sensitive to the detection of binaries in the angular separation regime between 0.03" and 5" with relatively bright companions (Delta V < 3). We report on the discovery of companions to 14 OB stars. In total we resolved companions of 41 of 385 O-stars (11%), 4 of 37 Wolf-Rayet stars (11%), and 89 of 139 B-stars (64%; an enriched visual binary sample that we selected for future orbital determinations). We made a statistical analysis of the binary frequency among the subsample that are listed in the Galactic O Star Catalog by compiling published data on other visual companions detected through adaptive optics studies and/or noted in the Washington Double Star Catalog and by collecting published information on radial velocities and spectroscopic binaries. We find that the binary frequency is much higher among O-stars in clusters and associations compared to the numbers for field and runaway O-stars, consistent with predictions for the ejection processes for runaway stars. We present a first orbit for the O-star Delta Orionis, a linear solution of the close, apparently optical, companion of the O-star Iota Orionis, and an improved orbit of the Be star Delta Scorpii. Finally, we list astrometric data for another 249 resolved and 221 unresolved targets that are lower mass stars that we observed for various other science programs.Comment: 76 pages, 6 figures, 11 table

Formation Scenario for Wide and Close Binary Systems

Fragmentation and binary formation processes are studied using three-dimensional resistive MHD nested grid simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we calculate the cloud evolution from the molecular cloud core (n=10^4 cm^-3) to the stellar core (n \simeq 10^22 cm^-3). We calculated 147 models with different initial magnetic, rotational, and thermal energies, and the amplitudes of the non-axisymmetric perturbation. In a collapsing cloud, fragmentation is mainly controlled by the initial ratio of the rotational to the magnetic energy, regardless of the initial thermal energy and amplitude of the non-axisymmetric perturbation. When the clouds have large rotational energies in relation to magnetic energies, fragmentation occurs in the low-density evolution phase (10^12 cm^-3 < n < 10^15 cm^-3) with separations of 3-300 AU. Fragments that appeared in this phase are expected to evolve into wide binary systems. On the other hand, fragmentation does not occur in the low-density evolution phase, when initial clouds have large magnetic energies in relation to the rotational energies. In these clouds, fragmentation only occurs in the high-density evolution phase (n > 10^17 cm^-3) after the clouds experience significant reduction of the magnetic field owing to Ohmic dissipation in the period of 10^12 cm^-3 < n < 10^15 cm^-3. Fragments appearing in this phase have separations of < 0.3 AU, and are expected to evolve into close binary systems. As a result, we found two typical fragmentation epochs, which cause different stellar separations. Although these typical separations are disturbed in the subsequent gas accretion phase, we might be able to observe two peaks of binary separations in extremely young stellar groups.Comment: 45 pages,12 figures, Submitted to ApJ, For high resolution figures see http://www2.scphys.kyoto-u.ac.jp/~machidam/protostar/proto/main-astroph.pd