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

Effect of timing and female quality on clutch size in the Collared Flycatcher Ficedula albicollis

Capsule: Laying date and female age appear to be related to clutch size. Aims: To test two hypotheses ('date' and 'quality'), which might explain why fewer eggs are laid late in the season. Methods: Four years of data and multivariate analysis were used to test the effects of timing of breeding and female quality reflected by morphological variables and age on clutch size in the Collared Flycatcher Ficedula albicollis. We estimated food supply during parental care by measuring diet composition of nestlings. Results: We distinguished the independent effects of date and age of females on clutch size. The type of prey fed to nestlings was different early and late in the season. Hence food supply during the nestling care period may be a limiting environmental factor that indirectly determines clutch size. Conclusion: Our results are consistent with the predictions of the date hypothesis, but the quality hypothesis was also partially supported. Depending on year effects, 30-50% of the variance in clutch size may be related to the timing of breeding and an additional 5-10% may be due to quality (age) differences between early- and late-breeding birds

Separation with restricted families of sets

Given a finite $n$-element set $X$, a family of subsets ${\mathcal F}\subset 2^X$ is said to separate $X$ if any two elements of $X$ are separated by at least one member of $\mathcal F$. It is shown that if $|\mathcal F|>2^{n-1}$, then one can select $\lceil\log n\rceil+1$ members of $\mathcal F$ that separate $X$. If $|\mathcal F|\ge \alpha 2^n$ for some $0<\alpha<1/2$, then $\log n+O(\log\frac1{\alpha}\log\log\frac1{\alpha})$ members of $\mathcal F$ are always sufficient to separate all pairs of elements of $X$ that are separated by some member of $\mathcal F$. This result is generalized to simultaneous separation in several sets. Analogous questions on separation by families of bounded Vapnik-Chervonenkis dimension and separation of point sets in ${\mathbb{R}}^d$ by convex sets are also considered.Comment: 13 page