A Generalisation of an Ostrowski Inequality in Inner Product Spaces

A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given

An Inequality in Metric Spaces

In this note we establish a general inequality valid in metric spaces that is related to the polygonal inequality and admits also a natural geometrical interpretation. Particular instances of interest holding in normed linear spaces and inner product spaces are pointed out as well

Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes

We consider the numerical solution of an inverse problem of finding the shape and location of holes in an elastic body. The problem is solved by minimizing a functional depending on the eigenvalues and traces of corresponding eigenmodes. We use the adjoint method to calculate the shape derivative of this functional. The optimization is performed by BFGS, using a genetic algorithm as a preprocessor and the Method of Fundamental Solutions as a solver for the direct problem. We address several numerical simulations that illustrate the good performance of the method.info:eu-repo/semantics/publishedVersio

The Spatial Clustering of Low Luminosity AGN

We present the first multi-parameter analysis of the narrow line AGN clustering properties. Estimates of the two-point correlation function (CF) based on SDSS DR2 data reveal that Seyferts are clearly less clustered than normal galaxies, while the clustering amplitude (r_0) of LINERs is consistent with that of the parent galaxy population. The similarities in the host properties (color and concentration index) of Seyferts and LINERs suggest that the difference in their r_0 is not driven by the morphology-density relation. We find that the luminosity of [O I] emission shows the strongest influence on AGN clustering, with low L([O I]) sources having the highest r_0. This trend is much stronger than the previously detected dependence on L([O III]), which we confirm. There is a strong correspondence between the clustering patterns of objects of given spectral type and their physical properties. LINERs, which exhibit high r_0, show the lowest luminosities and obscuration levels, and relatively low gas densities (n_e), suggesting that these objects harbor black holes that are relatively massive yet weakly active or inefficient in their accretion, probably due to the insufficiency of their fuel supply. Seyferts, which have low r_0, are luminous and show large n_e, suggesting that their black holes are less massive but accrete quickly and efficiently enough to clearly dominate the ionization. The low r_0 of the H II galaxies can be understood as a consequence of both the morphology-density and star formation rate-density relations, however, their spectral properties suggest that their centers hide amidst large amounts of obscuring material black holes of generally low mass whose activity remains relatively feeble. Our own Milky Way may be a typical such case.[abridged]Comment: 27 pages, color figures, some are severely degraded in resolution, emulateapj. See http://www.physics.drexel.edu/~constant/work/agnclustering.ps for high resolution version. Accepted to Ap

Spectral Properties of Galaxies in Void Regions

We present a study of spectral properties of galaxies in underdense large-scale structures, voids. Our void galaxy sample (75,939 galaxies) is selected from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) with $\rm z < 0.107$. We find that there are no significant differences in the luminosities, stellar masses, stellar populations, and specific star formation rates between void galaxies of specific spectral types and their wall counterparts. However, the fraction of star-forming galaxies in voids is significantly higher ($\ge 9\%$) than that in walls. Void galaxies, when considering all spectral types, are slightly fainter, less massive, have younger stellar populations and of higher specific star formation rates than wall galaxies. These minor differences are totally caused by the higher fraction of star-forming galaxies in voids. We confirm that AGNs exist in voids, already found by \cite{co08}, with similar abundance as in walls. Type I AGNs contribute $\sim$ 1\%-2\% of void galaxies, similar to their fraction in walls. The intrinsic [O III] luminosities , spanning over 10^6\ L_{\sun} \sim 10^9\ L_{\sun}, and Eddington ratios are similar comparing our void AGNs versus wall AGNs. Small scale statistics show that all spectral types of void galaxies are less clustered than their counterparts in walls. Major merger may not be the dominant trigger of black hole accretion in the luminosity range we probe. Our study implies that the growth of black holes relies weakly on large scale structures.Comment: 14 pages,16 figures, accepted for publication in Ap

Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with the symmetry group $O(1,1)\times SO(2)$, we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the $2\to 2$-scattering amplitude in $\cos\Theta$, $\Theta$ being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross-section are also presented.Comment: 25 page