Global Optimization for a Class of Nonlinear Sum of Ratios Problem

We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions

A comparison of different cluster mass estimates: consistency or discrepancy ?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and their dynamical evolution. Using a hitherto largest sample of lensing clusters drawn from literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is an excellent agreement between the weak lensing, X-ray and isothermal sphere model determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2--4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters as well as an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.Comment: 16 pages with 7 PS figures, MNRAS in pres

Structure, Luminescence, and Transport Properties of EuVO_4

Metastable scheelite EuVO_4 was stabilized by a high temperature and pressure method, which was transformed into a stable zircon phase by annealing treatment in air. Scheelite EuVO_4 gave strong emissions with a dominant peak at 617 nm associated with the ^(5)D_0-^(7)F_2 transition of Eu^(3+). ^(151)Eu Mössbauer spectra indicated that the isomer shift for the metastable scheelite phase was ca. 0.5 mm/s lower than that for the zircon phase, which was ascribed to a reduced covalency in the Eu-O bond originated via a charge transfer from oxygen to Eu3+ in scheelite lattice by producing an enhanced shielding of 4f electrons on the s orbital as well as a decrease in s electron density around Eu^(3+) nucleus. Impedance spectra for the zircon phase clearly demonstrated an ionic hopping in the bulk with a conductivity of ca. 1.0×10^(–3) S cm^(–1) at 500°C. EuVO_4 is proved to be both a potential phosphor and a potential ionic conductor