Phase statistics of the WMAP 7 year data

We performed a comprehensive statistical analysis using complex phases of the a_lm coefficients computed from the most recent data of the Wilkinson Microwave Anisotropy Probe (WMAP). Our aim was to confirm or constrain the presence of non-Gaussianities in the data. We found phase correlations - that suggest non-Gaussianity - at high-l in a_lm coefficients by applying various statistical tests. Most of all, we detected a non-Gaussian signal reaching a significance of 4.7 sigma using random walk statistics and simulations. However, our conclusion is that the non-Gaussian behavior is due to contamination from galactic foregrounds that show up in small scales only. When masked out the contaminated regions, we found no significant non-Gaussianity. Furthermore, we constrained the f_NL parameter using CMB simulations that mimic primordial non-Gaussianity. Our estimate is f_NL=40 +/- 200, in agreement with previous measurements and inflationary expectations.Comment: 4 pages, 4 figures, Accepted for Publication in A

Ball and Spindle Convexity with respect to a Convex Body

Let $C\subset {\mathbb R}^n$ be a convex body. We introduce two notions of convexity associated to C. A set $K$ is $C$-ball convex if it is the intersection of translates of $C$, or it is either $\emptyset$, or ${\mathbb R}^n$. The $C$-ball convex hull of two points is called a $C$-spindle. $K$ is $C$-spindle convex if it contains the $C$-spindle of any pair of its points. We investigate how some fundamental properties of conventional convex sets can be adapted to $C$-spindle convex and $C$-ball convex sets. We study separation properties and Carath\'eodory numbers of these two convexity structures. We investigate the basic properties of arc-distance, a quantity defined by a centrally symmetric planar disc $C$, which is the length of an arc of a translate of $C$, measured in the $C$-norm, that connects two points. Then we characterize those $n$-dimensional convex bodies $C$ for which every $C$-ball convex set is the $C$-ball convex hull of finitely many points. Finally, we obtain a stability result concerning covering numbers of some $C$-ball convex sets, and diametrically maximal sets in $n$-dimensional Minkowski spaces.Comment: 27 pages, 5 figure

Numerical investigation of the dynamics of linear spin ss fields on Kerr background I. Late time tails of spin s=±1,±2s = \pm 1, \pm 2 fields

The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics which allows us to evaluate all the angular derivatives analytically, whereas the evolution of the expansion coefficients, in the time-radial section, is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations single mode excitations---either static or purely dynamical type initial data---are applied. Within this setup the late time tail behavior is investigated. Due to the applied conformal compactification the asymptotic decay rates are determined at three characteristic locations---in the domain of outer communication, at the event horizon and at future null infinity---simultaneously. Recently introduced new type of `energy' and `angular momentum' balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema, and also to verify the proper implementation of the underlying mathematical model.Comment: 38 pages, 5 figures, typos correcte

Customer Loyalty Problems in Retail Banking

According to analyses of the most business consulting companies (KPMG, Capgemini, Deloitte, TowerGroup, etc.) customers are discontented with the retail banking experience. To achieve higher business growth, banks must increase customer loyalty by delivering a distinctive experience that combines the right mix of convenience, value and service and forges an emotional bond with consumers. Winners will be those that transform themselves into customer-centric enterprises by having a clear vision of what they want to achieve, fully aligning business processes and IT infrastructure to achieve those goals and engaging their employees in the process. The first step to do it is the identification of customer satisfaction. This paper intends to reveal its essential elements.customer loyalty, customer attitudes, retail banking