A note on eigenvalues location for trace zero doubly stochastic matrices

Some results on the location of the eigenvalues of trace zero doubly stochastic matrices are provided. A result similar to that provided in [H. Perfect and L. Mirsky. Spectral properties of doubly–stochastic matrices. Monatshefte f¨ur Mathematik, 69(1):35–57, 1965.] for doubly stochastic matrices is given

An efficient algorithm for positive realizations

We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one of which complements an earlier result of \cite{large}. Finally, we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed efficient in general

Spectroscopic observations of comet Kohoutek (1973f), 2

Spectroscopic observations of comet Kohoutek at the Asiago Astrophysical Observatory are described. Spectra cover six nights before perihelion and five nights after perihelion. The spectra of the coma and tail of comet Kohoutek are characterized by fairly strong, asymmetric H2O(+) emissions in the red and the near infrared spectral regions and by the appearance of the 01 forbidden lines at 6300-6364 A, already at heliocentric distance r=1.55 A.U. These peculiarities suggest that some differences in chemical abundances or in physical conditions exist between comet Kohoutek and other comets

The complex of pant decompositions of a surface

We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex. Our construction, unlike the previous ones, keeps the arguments concerning the structural transformations independent from those deriving from the action of the mapping class group. The moves and the relations turn out to be supported in subsurfaces with 3g-3+n=1,2 (where g is the genus and n is the number of boundary components), illustrating in this way the so called Grothendieck principle.Comment: Minor changes in the introductio

Conformal Manifolds for the Conifold and other Toric Field Theories

In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this "conformal manifold". We identify the conformal manifold for all the Y^{p,q} toric singularities, paying special attention to the case of the conifold, Y^{1,0}. For a general Y^{p,q} the conformal manifold is three dimensional, while for the conifold it is five dimensional. There is always an exactly marginal deformation, analogous to the beta-deformation of N=4 SYM, which involves fluxes in the dual gravity description. This beta-deformation exists for any toric Calabi-Yau singularity.Comment: 30 pages, 5 figures; V2: References added, minor change

A multi-wavelength study of the starburst galaxy NGC 7673

HST/WFPC2 images resolved NGC 7673 into a large number of star clusters. Among these, 31 fall inside the IUE large aperture, which was used to acquire an integrated ultraviolet spectrum of the galaxy. We have fitted Starburst99 evolutionary synthesis models to the observed colours of these clusters and derived ages, reddenings, and masses of the clusters. Then a simple sum of the clusters synthetic UV spectra has been compared to the observed IUE spectrum, in order to investigate the star formation history of NGC 7673.Comment: 6 pages, 2 figures, to appear in the Proceedings of the Conference "Starburst-from 30 Doradus to Lyman Break Galaxies

BPS Solutions in AdS/CFT

We study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. We analyse the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound. We also show how the same formalism is suitable for the description of the AdS_5 x Y^{p,q} geometries and a class of their excitations.Comment: 5 pages, Latex, uses w-art class (included). To appear in the Proceedings of the RTN workshop "ForcesUniverse", Naples, October 9-13, 200