On the theory of Gordan-Noether on homogeneous forms with zero Hessian (Improved version)

We give a detailed proof for Gordan-Noether's results in "Ueber die algebraischen Formen, deren Hesse'sche Determinante identisch verschwindet" published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a similar direction as the present paper, but did not provide a proof for every result. In our paper, every result is proved. Furthermore, our paper is independent of Lossen's paper and includes a considerable number of new observations. An earlier version of this paper has been printed in Proceedings of the School of Science of Tokai University, Vol.49, Mar. 2014. In this version, a serious error has been corrected and some new results have been added

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Auszug zweier Schreiben des Prof. Hesse an den Herrn Prof. Jacobi und eines Schreibens des Prof. Jacobi an Herrn Prof. Hesse.

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INTEGRAL observations of the black hole candidate H 1743-322 in outburst

INTEGRAL made 3 observations in 2003 April of the black hole candidate H 1743-322 during the rising part, and close to the maximum, of an outburst. H 1743-322 was previously observed in outburst in 1977-1978. The source is located in a crowded region of the sky (l = 357 deg, b = -2 deg) and at least 18 sources are clearly detected in the field of view of the gamma-ray imager during a 277 ksec exposure. These are well known persistent X-ray binaries and 3 transient sources in outburst. The combined 5-200 keV JEM-X and SPI spectrum of H 1743-322 is well fit with an absorbed ((2.5 10E22 atom/cm2) soft (photon index 2.70 +/- 0.09) power-law model consistent with J 1743-322 being in a high/soft state.Comment: 5 pages. Figs. 2 and 3 are best viewed in color. To appear in INTEGRAL special edition of A&A

Equianalytic and equisingular families of curves on surfaces

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are mainly concerned with analytic resp. topological singularity types and give a sufficient condition for the smoothness of H (at C). Our results for S=P^2 seem to be quite sharp for families of cuves of small degree d.Comment: LaTeX v 2.0

Electron scale structures and magnetic reconnection signatures in the turbulent magnetosheath

Collisionless space plasma turbulence can generate reconnecting thin current sheets as suggested by recent results of numerical magnetohydrodynamic simulations. The MMS mission provides the first serious opportunity to check if small ion-electron-scale reconnection, generated by turbulence, resembles the reconnection events frequently observed in the magnetotail or at the magnetopause. Here we investigate field and particle observations obtained by the MMS fleet in the turbulent terrestrial magnetosheath behind quasi-parallel bow shock geometry. We observe multiple small-scale current sheets during the event and present a detailed look of one of the detected structures. The emergence of thin current sheets can lead to electron scale structures where ions are demagnetized. Within the selected structure we see signatures of ion demagnetization, electron jets, electron heating and agyrotropy suggesting that MMS spacecraft observe reconnection at these scales

First INTEGRAL Observations of Eight Persistent Neutron Star Low Mass X-ray Binaries

Early results from the INTEGRAL Core Program, for a sample of eight persistently bright neutron star low mass X-ray binaries in the energy range from 5 keV to 200 keV are presented. It is shown that INTEGRAL efficiently detects sources and that spectra may be obtained up to several hundreds of keV by combining data from three of the four INTEGRAL instruments: JEM-X, IBIS and SPI. For the source GX 17+2 it is shown that the spectrum extends well above 100 keV with a flattening of the spectrum above 30 keV. This might suggest a non-thermal comptonisation emission, but uncertainties in the current data reduction and background determination do not allow firm conclusions to be drawn.Comment: 5 pages, 6 figures, accepted for publication in Astronomy & Astrophysic