XMM-Newton temperature maps for five intermediate redshift clusters of galaxies

We have analyzed XMM-Newton archive data for five clusters of galaxies (redshifts 0.223-0.313) covering a wide range of dynamical states, from relaxed objects to clusters undergoing several mergers. We present here temperature maps of the X-ray gas together with a preliminary interpretation of the formation history of these clusters. (c) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Further probing the nature of FSR 1767

With Two-Micron All-Sky Survey (2MASS) photometry and proper motions, Bonatto et al. suggested that FSR 1767 is a globular cluster (GC), while with J and K NTT/SOFI photometry Froebrich, Meusinger & Scholz concluded that it is not a star cluster. In this study, we combine previous and new evidence that are consistent with a GC. For instance, we show that the horizontal branch (HB) and red giant branch (RGB) stars, besides sharing a common proper motion, have radial density profiles that consistently follow the King`s law independently. Reddening maps around FSR 1767 are built using the bulge RGB as reference and also Schlegel`s extinction values to study local absorptions. Both approaches provide similar maps and show that FSR 1767 is not located in a dust window, which otherwise might have produced the stellar overdensity. Besides, neighbouring regions of similar reddening as FSR 1767 do not present the blue HB stars that are a conspicuous feature in the colour-magnitude diagram of FSR 1767. We report the presence of a compact group of stars located in the central parts of FSR 1767. It appears to be a detached post-collapse core, similar to those of other nearby low-luminosity GCs projected towards the bulge. We note that while the NTT/SOFI photometry of the star cluster FSR 1716 matches perfectly that from 2MASS, it shows a considerable offset for FSR 1767. We discuss the possible reasons why both photometries differ. We confirm our previous structural and photometric fundamental parameters for FSR 1767, which are consistent with a GC.

Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

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.